simplify (sqrt(5))/(sqrt(6)+2)-2/(5sqrt(3))

{ "query": { "display": "simplify $$\\frac{\\sqrt{5}}{\\sqrt{6}+2}-\\frac{2}{5\\sqrt{3}}$$", "symbolab_question": "SIMPLIFY#simplify \\frac{\\sqrt{5}}{\\sqrt{6}+2}-\\frac{2}{5\\sqrt{3}}" }, "solution": { "level": "PERFORMED", "subject": "Algebra", "topic": "Algebra", "subTopic": "Simplify", "default": "\\frac{15\\sqrt{10}-10\\sqrt{15}-4}{10\\sqrt{3}}", "decimal": "0.27160…", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\frac{\\sqrt{5}}{\\sqrt{6}+2}-\\frac{2}{5\\sqrt{3}}=\\frac{15\\sqrt{10}-10\\sqrt{15}-4}{10\\sqrt{3}}$$", "input": "\\frac{\\sqrt{5}}{\\sqrt{6}+2}-\\frac{2}{5\\sqrt{3}}", "steps": [ { "type": "interim", "title": "Cancel $$\\frac{\\sqrt{5}}{\\sqrt{6}+2}:{\\quad}\\frac{\\sqrt{30}-2\\sqrt{5}}{2}$$", "input": "\\frac{\\sqrt{5}}{\\sqrt{6}+2}", "steps": [ { "type": "step", "primary": "Multiply by the conjugate $$\\frac{\\sqrt{6}-2}{\\sqrt{6}-2}$$", "result": "=\\frac{\\sqrt{5}\\left(\\sqrt{6}-2\\right)}{\\left(\\sqrt{6}+2\\right)\\left(\\sqrt{6}-2\\right)}" }, { "type": "interim", "title": "Expand $$\\sqrt{5}\\left(\\sqrt{6}-2\\right):{\\quad}\\sqrt{30}-2\\sqrt{5}$$", "input": "\\sqrt{5}\\left(\\sqrt{6}-2\\right)", "steps": [ { "type": "step", "primary": "Apply the distributive law: $$a\\left(b-c\\right)=ab-ac$$", "secondary": [ "$$\\sqrt{5}\\left(\\sqrt{6}-2\\right)=\\sqrt{5}\\sqrt{6}-\\sqrt{5}\\cdot\\:2$$" ], "result": "=\\sqrt{5}\\sqrt{6}-\\sqrt{5}\\cdot\\:2", "meta": { "practiceLink": "/practice/expansion-practice", "practiceTopic": "Expand Rules" } }, { "type": "interim", "title": "$$\\sqrt{5}\\sqrt{6}-\\sqrt{5}\\cdot\\:2=\\sqrt{30}-2\\sqrt{5}$$", "input": "\\sqrt{5}\\sqrt{6}-\\sqrt{5}\\cdot\\:2", "steps": [ { "type": "step", "result": "=\\sqrt{5}\\sqrt{6}-2\\sqrt{5}" }, { "type": "interim", "title": "$$\\sqrt{5}\\sqrt{6}=\\sqrt{30}$$", "input": "\\sqrt{5}\\sqrt{6}", "steps": [ { "type": "step", "primary": "Apply radical rule: $$\\sqrt{a}\\sqrt{b}=\\sqrt{ab},\\:\\quad\\:a\\ge0,\\:b\\ge0$$", "secondary": [ "$$\\sqrt{5}\\sqrt{6}=\\sqrt{5\\cdot\\:6}$$" ], "result": "=\\sqrt{5\\cdot\\:6}" }, { "type": "step", "primary": "Multiply the numbers: $$5\\cdot\\:6=30$$", "result": "=\\sqrt{30}" } ], "meta": { "solvingClass": "Solver2", "interimType": "Solver2", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7XmafnKnZ8vS4hnzkiX6j/Z7d8gbO3MLDrjYuTJHkSmvMwViaLUXkeD+JukROhWdj++u9/qVfxQagc6QWDR5itbtCR5dIjxQ5ASg+ZPFVSscjKU7nIuMZ1yeEmFWKYfsYUr/WRn+evMi0YDuExuV2Qw==" } }, { "type": "step", "result": "=\\sqrt{30}-2\\sqrt{5}" } ], "meta": { "solvingClass": "Solver2", "interimType": "Solver2", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7XmafnKnZ8vS4hnzkiX6j/YyYBJRWKX2WaWcBjTSF+Bvt9BcJfUCjyccjv0xUQm+Rq47vuWedXv2WUg94ER8IwQZ/AnAepl5nZ1I1BmTjJzzgYe7O4EOHkgqcEVclB+y0rgvfyOtEodFH37m15lO+gLLD8XGLfw10RV6ACFjco3hoUDPx1nKqi8rVAZiOIWheuQ6T4WQ/RQSdfRtkDULzbhxV9o1Rs2e9AedtRObhpig=" } }, { "type": "step", "result": "=\\sqrt{30}-2\\sqrt{5}" } ], "meta": { "interimType": "Generic Expand Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7ECl81GL+sHp+UX1O7owT7axMYXkf3zZNdxF3AjpOqoYLAZlDhoAdFQF6AF4pPagvRKAKbro8EavzLN8GuIDU/PWVUjtAdd6EqSvsyX6r+5AezFilETfuNygjs0XPkV2hfBb3dXlBc4zEpP3O1+L+GKYCMNVydKHOaQ0LBo3PvBI=" } }, { "type": "interim", "title": "Expand $$\\left(\\sqrt{6}+2\\right)\\left(\\sqrt{6}-2\\right):{\\quad}2$$", "input": "\\left(\\sqrt{6}+2\\right)\\left(\\sqrt{6}-2\\right)", "steps": [ { "type": "interim", "title": "Apply Difference of Two Squares $$\\left(\\sqrt{6}+2\\right)\\left(\\sqrt{6}-2\\right):{\\quad}2$$", "input": "\\left(\\sqrt{6}+2\\right)\\left(\\sqrt{6}-2\\right)", "steps": [ { "type": "step", "primary": "Apply Difference of Two Squares Formula: $$\\left(a+b\\right)\\left(a-b\\right)=a^2-b^2$$", "secondary": [ "$$\\left(\\sqrt{6}+2\\right)\\left(\\sqrt{6}-2\\right)=\\left(\\sqrt{6}\\right)^{2}-2^{2}$$" ], "result": "=\\left(\\sqrt{6}\\right)^{2}-2^{2}", "meta": { "practiceLink": "/practice/expansion-practice#area=main&subtopic=Difference%20of%20Two%20Squares", "practiceTopic": "Expand Difference of Squares" } }, { "type": "interim", "title": "$$\\left(\\sqrt{6}\\right)^{2}-2^{2}=2$$", "input": "\\left(\\sqrt{6}\\right)^{2}-2^{2}", "steps": [ { "type": "interim", "title": "$$\\left(\\sqrt{6}\\right)^{2}=6$$", "input": "\\left(\\sqrt{6}\\right)^{2}", "steps": [ { "type": "step", "primary": "Apply exponent rule: $$\\left(\\sqrt[n]{a}\\right)^n=a,\\:\\quad\\:n\\:is\\:odd\\:or\\:a\\ge0$$", "secondary": [ "$$\\left(\\sqrt{6}\\right)^{2}=6$$" ], "result": "=6" } ], "meta": { "interimType": "N/A" } }, { "type": "interim", "title": "$$2^{2}=4$$", "input": "2^{2}", "steps": [ { "type": "step", "primary": "$$2^{2}=4$$", "result": "=4" } ], "meta": { "interimType": "N/A" } }, { "type": "step", "result": "=6-4" }, { "type": "step", "primary": "Subtract the numbers: $$6-4=2$$", "result": "=2" } ], "meta": { "solvingClass": "Solver2", "interimType": "Solver2", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7srZuGI+Q8Iw6MX6TyHGHi31MpdtjtJQsW3dru8jz+JMJQJZuTAY5js+oqjdT8kslA/3mcjG3O2OfW1lteIMatXUPSnNvSQxR498B9h9qjkzI3S8oYAPC3kKTa50ePate" } }, { "type": "step", "result": "=2" } ], "meta": { "solvingClass": "Solver2", "interimType": "Expand Difference Squares Rule Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7O62yKKtC6+yKjUNmPFBt99FhVvvH6bkU1i4UNl1HLAv10mRp2XzAVYQ4Un4WqZF17bk8wvWUuXU/PEZ9CQUgOcG6tojj+JfsMopZLD45KVf2NDAfsyIaCZ92Q7dhj/ZLwuvn36lcrSbdF0eJL9ZKpFIG/qLOF4tVQpD96aiQBTKlfF5zpwtVdF/UEDoNRLsWZpj9JsLG7phjL+8oRhl/VsyHbYj7yGr8JWWMsG67VAGBUXheC39hpCoZzxknj8Ul" } }, { "type": "step", "result": "=2" } ], "meta": { "interimType": "Generic Expand Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7vz0OwVmz7FbkxdUH+eNAiT3N5NaVi8HrXvI7UpENUKafBLWE3vHgh6h28KMZoXHVdQxShwOg3W+URNAMu5sPa6VYwrogLl29RT6HYd2NJ316pfF1z6umzUJTJvt+ojYZjmLRtfamxNlPDopLD4I+m/0ZBgscUc92EI2mAb7808AIp6WqkUdPXuXSkAcvEgr0" } }, { "type": "step", "result": "=\\frac{\\sqrt{30}-2\\sqrt{5}}{2}" } ], "meta": { "solvingClass": "Solver2", "interimType": "Generic Cancel Title 1Eq" } }, { "type": "step", "result": "=\\frac{\\sqrt{30}-2\\sqrt{5}}{2}-\\frac{2}{5\\sqrt{3}}" }, { "type": "interim", "title": "$$\\frac{\\sqrt{30}-2\\sqrt{5}}{2}-\\frac{2}{5\\sqrt{3}}=\\frac{\\left(\\sqrt{30}-2\\sqrt{5}\\right)\\cdot\\:5\\sqrt{3}-4}{10\\sqrt{3}}$$", "input": "\\frac{\\sqrt{30}-2\\sqrt{5}}{2}-\\frac{2}{5\\sqrt{3}}", "steps": [ { "type": "interim", "title": "Least Common Multiplier of $$2,\\:5\\sqrt{3}:{\\quad}10\\sqrt{3}$$", "input": "2,\\:5\\sqrt{3}", "steps": [ { "type": "definition", "title": "Lowest Common Multiplier (LCM)", "text": "The LCM of $$a,\\:b\\:$$is the smallest multiplier that is divisible by both $$a$$ and $$b$$" }, { "type": "interim", "title": "Least Common Multiplier of $$2,\\:5:{\\quad}10$$", "input": "2,\\:5", "steps": [ { "type": "definition", "title": "Least Common Multiplier (LCM)", "text": "The LCM of $$a,\\:b$$ is the smallest positive number that is divisible by both $$a$$ and $$b$$" }, { "type": "interim", "title": "Prime factorization of $$2:{\\quad}2$$", "input": "2", "steps": [ { "type": "step", "primary": "$$2$$ is a prime number, therefore no factorization is possible", "result": "=2" } ], "meta": { "solvingClass": "Composite Integer", "interimType": "Prime Fac 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3PHQdChPJ2JhfqHT+ZU0OMrfn8NOj0LUzuzje6xTyxRl8ZboA8wPLg0yhI4RzfjFw/y9DKGIPglJ+qMi9xDu2KE1OovxZAaXg7BtrFPk4UcCzRnGgMN6CYRfod7Mq0dp1+G9v2aKasChgV65VW8cTW" } }, { "type": "interim", "title": "Prime factorization of $$5:{\\quad}5$$", "input": "5", "steps": [ { "type": "step", "primary": "$$5$$ is a prime number, therefore no factorization is possible", "result": "=5" } ], "meta": { "solvingClass": "Composite Integer", "interimType": "Prime Fac 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3PHQdChPJ2JhfqHT+ZU0OMrfn8NOj0LUzuzje6xTyxRjl/dE9e0owjU0NK6lxSAv4/y9DKGIPglJ+qMi9xDu2KE1OovxZAaXg7BtrFPk4UcCzRnGgMN6CYRfod7Mq0dp3mWpvzkJh0pk9SzVPr3Sj8" } }, { "type": "step", "primary": "Multiply each factor the greatest number of times it occurs in either $$2$$ or $$5$$", "result": "=2\\cdot\\:5" }, { "type": "step", "primary": "Multiply the numbers: $$2\\cdot\\:5=10$$", "result": "=10" } ], "meta": { "solvingClass": "LCM", "interimType": "LCM Top 1Eq" } }, { "type": "step", "primary": "Compute an expression comprised of factors that appear either in $$2$$ or $$5\\sqrt{3}$$", "result": "=10\\sqrt{3}" } ], "meta": { "solvingClass": "LCM", "interimType": "LCM Top 1Eq" } }, { "type": "interim", "title": "Adjust Fractions based on the LCM", "steps": [ { "type": "step", "primary": "Multiply each numerator by the same amount needed to multiply its<br/>corresponding denominator to turn it into the LCM $$10\\sqrt{3}$$" }, { "type": "step", "primary": "For $$\\frac{\\sqrt{30}-2\\sqrt{5}}{2}:\\:$$multiply the denominator and numerator by $$5\\sqrt{3}$$", "result": "\\frac{\\sqrt{30}-2\\sqrt{5}}{2}=\\frac{\\left(\\sqrt{30}-2\\sqrt{5}\\right)\\cdot\\:5\\sqrt{3}}{2\\cdot\\:5\\sqrt{3}}=\\frac{\\left(\\sqrt{30}-2\\sqrt{5}\\right)\\cdot\\:5\\sqrt{3}}{10\\sqrt{3}}" }, { "type": "step", "primary": "For $$\\frac{2}{5\\sqrt{3}}:\\:$$multiply the denominator and numerator by $$2$$", "result": "\\frac{2}{5\\sqrt{3}}=\\frac{2\\cdot\\:2}{5\\sqrt{3}\\cdot\\:2}=\\frac{4}{10\\sqrt{3}}" } ], "meta": { "interimType": "LCD Adjust Fractions 1Eq" } }, { "type": "step", "result": "=\\frac{\\left(\\sqrt{30}-2\\sqrt{5}\\right)\\cdot\\:5\\sqrt{3}}{10\\sqrt{3}}-\\frac{4}{10\\sqrt{3}}" }, { "type": "step", "primary": "Apply the fraction rule: $$\\frac{a}{c}-\\frac{b}{c}=\\frac{a-b}{c}$$", "result": "=\\frac{\\left(\\sqrt{30}-2\\sqrt{5}\\right)\\cdot\\:5\\sqrt{3}-4}{10\\sqrt{3}}" } ], "meta": { "solvingClass": "Solver2", "interimType": "Solver2", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s74DwjiBDVBIb8+yh6fkkMMX2AdrpPBz9rU86RCq9xPHb/BCGx3SuU7MZUfakpCSD9DlU2Th8/Ot0BkPrMiKMYRnWD310L1+P2yDQQfMEhENEEkvPsajhMhcVdAT5G4T4FuQ6T4WQ/RQSdfRtkDULzbvALk+gzz2L06P+742NhARyhD5E8hGPCfgnGRJabR2ua0zMYqEwpcuv4TrlApQ7epommCeZg/vYI25xQTJ4ImcFYqDfe2SGKqvEVUnYTO/9WqBXzmLIgIzYQAVAcf2mv0h51lrMF7J+KCG65Eiff6u96iXWmeK8nMUBDHbP+vRaFkqDrIQUKVMCWWdVNqf0/QUyc3/HRPJ7EAbF8f2T3JAcSzFICX48y6okHYolpWtZF" } }, { "type": "step", "result": "=\\frac{\\left(\\sqrt{30}-2\\sqrt{5}\\right)\\cdot\\:5\\sqrt{3}-4}{10\\sqrt{3}}" }, { "type": "interim", "title": "Simplify $$\\left(\\sqrt{30}-2\\sqrt{5}\\right)\\cdot\\:5\\sqrt{3}-4:{\\quad}15\\sqrt{10}-10\\sqrt{15}-4$$", "input": "\\left(\\sqrt{30}-2\\sqrt{5}\\right)\\cdot\\:5\\sqrt{3}-4", "steps": [ { "type": "step", "result": "=5\\sqrt{3}\\left(\\sqrt{30}-2\\sqrt{5}\\right)-4" }, { "type": "interim", "title": "Expand $$5\\sqrt{3}\\left(\\sqrt{30}-2\\sqrt{5}\\right):{\\quad}15\\sqrt{10}-10\\sqrt{15}$$", "input": "5\\sqrt{3}\\left(\\sqrt{30}-2\\sqrt{5}\\right)", "steps": [ { "type": "step", "primary": "Apply the distributive law: $$a\\left(b-c\\right)=ab-ac$$", "secondary": [ "$$5\\sqrt{3}\\left(\\sqrt{30}-2\\sqrt{5}\\right)=5\\sqrt{3}\\sqrt{30}-5\\sqrt{3}\\cdot\\:2\\sqrt{5}$$" ], "result": "=5\\sqrt{3}\\sqrt{30}-5\\sqrt{3}\\cdot\\:2\\sqrt{5}", "meta": { "practiceLink": "/practice/expansion-practice", "practiceTopic": "Expand Rules" } }, { "type": "interim", "title": "$$5\\sqrt{3}\\sqrt{30}-5\\sqrt{3}\\cdot\\:2\\sqrt{5}=15\\sqrt{10}-10\\sqrt{15}$$", "input": "5\\sqrt{3}\\sqrt{30}-5\\sqrt{3}\\cdot\\:2\\sqrt{5}", "steps": [ { "type": "step", "primary": "Multiply the numbers: $$5\\cdot\\:2=10$$", "result": "=5\\sqrt{3}\\sqrt{30}-10\\sqrt{3}\\sqrt{5}" }, { "type": "interim", "title": "$$5\\sqrt{3}\\sqrt{30}=15\\sqrt{10}$$", "input": "5\\sqrt{3}\\sqrt{30}", "steps": [ { "type": "interim", "title": "$$5\\sqrt{3}\\sqrt{30}=5\\cdot\\:3\\sqrt{10}$$", "input": "5\\sqrt{3}\\sqrt{30}", "steps": [ { "type": "interim", "title": "$$\\sqrt{30}=\\sqrt{3}\\sqrt{10}$$", "input": "\\sqrt{30}", "steps": [ { "type": "step", "primary": "Factor the number: $$30=3\\cdot\\:10$$", "result": "=\\sqrt{3\\cdot\\:10}" }, { "type": "step", "primary": "Apply radical rule: $$\\sqrt{ab}=\\sqrt{a}\\sqrt{b},\\:\\quad\\:a\\ge0,\\:b\\ge0$$", "secondary": [ "$$\\sqrt{3\\cdot\\:10}=\\sqrt{3}\\sqrt{10}$$" ], "result": "=\\sqrt{3}\\sqrt{10}" } ], "meta": { "solvingClass": "Solver2", "interimType": "Solver2", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7RLA6HYW5m+Fwe4gGEetLBiAn9lkDfZkicUGkO3EF+IpIyB7h/T9zVR3i5g4dJo871uVtVez0+610qBPt0GmmSIY+spUsB4yZJkDyh9+Pu38aBcuuHDcYMJAP1PALAgV4ChOSOCYnzVArfbRnt49gXg==" } }, { "type": "step", "result": "=5\\sqrt{3}\\sqrt{3}\\sqrt{10}" }, { "type": "step", "primary": "Apply radical rule: $$\\sqrt{a}\\sqrt{a}=a,\\:\\quad\\:a\\ge0$$", "secondary": [ "$$\\sqrt{3}\\sqrt{3}=3$$" ], "result": "=5\\cdot\\:3\\sqrt{10}" } ], "meta": { "solvingClass": "Solver2", "interimType": "Solver2", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7YC1q9TPnLtSeErcRoU9gk8eN0L/qkQYs4T7vS4Y8FHOrju+5Z51e/ZZSD3gRHwjBKv5/kGRNPFuIY4XH4WVLnmrN9fOQHas0CiPpFAZIyVEKum8TwmJ1TeSlGstL+WkaHH2R5Cb/TA4YiX2/Qfv9kSArD8yingMc304lwkNHRWMkt3WiGR7ZaCaXvz77bMjS" } }, { "type": "step", "result": "=5\\cdot\\:3\\sqrt{10}" }, { "type": "step", "primary": "Multiply the numbers: $$5\\cdot\\:3=15$$", "result": "=15\\sqrt{10}" } ], "meta": { "interimType": "N/A" } }, { "type": "interim", "title": "$$\\sqrt{3}\\sqrt{5}=\\sqrt{15}$$", "input": "\\sqrt{3}\\sqrt{5}", "steps": [ { "type": "step", "primary": "Apply radical rule: $$\\sqrt{a}\\sqrt{b}=\\sqrt{ab},\\:\\quad\\:a\\ge0,\\:b\\ge0$$", "secondary": [ "$$\\sqrt{3}\\sqrt{5}=\\sqrt{3\\cdot\\:5}$$" ], "result": "=\\sqrt{3\\cdot\\:5}" }, { "type": "step", "primary": "Multiply the numbers: $$3\\cdot\\:5=15$$", "result": "=\\sqrt{15}" } ], "meta": { "interimType": "N/A" } }, { "type": "step", "result": "=15\\sqrt{10}-10\\sqrt{15}" } ], "meta": { "solvingClass": "Solver2", "interimType": "Solver2" } }, { "type": "step", "result": "=15\\sqrt{10}-10\\sqrt{15}" } ], "meta": { "solvingClass": "Solver2", "interimType": "Generic Expand Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7gzxCd0OfSZlUrY+Uy1X5rlqNoxvEwl5uuMZqPtq96NdnSBQ88Vqz7BhiG/DaGWpUifR0Hzd6jnwAeJAXfVDhQ6QO3JZEDmu86GRCA4IEhuFkS3dlcCKpQTQcheuut7Mkw+/0w1fjHXEdBnTevtRQ7eW+Ln7oE3pt/QGoYdPhvatYqDfe2SGKqvEVUnYTO/9W4gBJl4WMO1rA0a30/bUYlg==" } }, { "type": "step", "result": "=15\\sqrt{10}-10\\sqrt{15}-4" } ], "meta": { "solvingClass": "Solver2", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7FFHpBdo4ca/lQAndg2ukG5Kg6yEFClTAllnVTan9P0HS26/sdoZ5Js3SEOFW6Rg5ICf2WQN9mSJxQaQ7cQX4ipdHV1RG2KtvHZwZ+m6HqnNbCz31EzG6Lvx1aSMhRmmh5j5gVFOqlSehWO587EUSx5jcBIL5pmo83UMFZRSzJsUFvz16ogd1fUFsBDQBySRiv37MjsezVkZ97SbqGgRFcAabtn/ZxBmRgP3NyTvsbmnk/uIB5yXjV0QE57O2LF0+" } }, { "type": "step", "result": "=\\frac{15\\sqrt{10}-10\\sqrt{15}-4}{10\\sqrt{3}}" } ], "meta": { "solvingClass": "Solver2" } }, "meta": { "showVerify": true } }