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Popular Algebra >

Simplify (2r^3s^8(7r^7-5r^3s^4)-(2r^10s^8-6r^6s^12))/(4r^2s^4)

Solution

simplify

\frac{( 2 r ^{3} s ^{8} ( 7 r ^{7} - 5 r ^{3} s ^{4} ) - ( 2 r ^{10} s ^{8} - 6 r ^{6} s ^{12} ) )}{( 4 r ^{2} s ^{4} )}

Solution

r^{4} s^{4} (3 r^{4} - s^{4})

Solution steps

\frac{2 r ^{3} s ^{8} ( 7 r ^{7} - 5 r ^{3} s ^{4} ) - ( 2 r ^{10} s ^{8} - 6 r ^{6} s ^{12} )}{4 r ^{2} s ^{4}}

Factor

2 r^{3} s^{8} (7 r^{7} - 5 r^{3} s^{4}) - (2 r^{10} s^{8} - 6 r^{6} s^{12}) : 4 r^{6} s^{8} (3 r^{4} - s^{4})

= \frac{4 r ^{6} s ^{8} ( 3 r ^{4} - s ^{4} )}{4 r ^{2} s ^{4}}

Cancel the common factor:

4

= \frac{r ^{6} s ^{8} ( 3 r ^{4} - s ^{4} )}{r ^{2} s ^{4}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

r^{6} = r^{2} r^{4}

= \frac{r ^{2} r ^{4} s ^{8} ( 3 r ^{4} - s ^{4} )}{r ^{2} s ^{4}}

Cancel the common factor:

r^{2}

= \frac{r ^{4} s ^{8} ( 3 r ^{4} - s ^{4} )}{s ^{4}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

s^{8} = s^{4} s^{4}

= \frac{r ^{4} s ^{4} s ^{4} ( 3 r ^{4} - s ^{4} )}{s ^{4}}

Cancel the common factor:

s^{4}

= r^{4} s^{4} (3 r^{4} - s^{4})

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\frac{64}{25}

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x, 5.5 - x = - 4.5 - x

Convert to a Decimal 33%simplify

33%

Solve Using the Quadratic Formula 3x^2-7x+4=0 quadratic formula

3 x^{2} - 7 x + 4 = 0

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n, 2 - 2 n = 3 n + 17

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