What is (6a^2+12ab-9a^4)/(3a^3b) ?

The solution to (6a^2+12ab-9a^4)/(3a^3b) is (2a+4b-3a^3)/(a^2b)

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simplify (6a^2+12ab-9a^4)/(3a^3b)

simplify

\frac{6 a ^{2} + 12 ab - 9 a ^{4}}{3 a ^{3} b}

\frac{2 a + 4 b - 3 a ^{3}}{a ^{2} b}

Solution steps

\frac{6 a ^{2} + 12 ab - 9 a ^{4}}{3 a ^{3} b}

Factor

6 a^{2} + 12 ab - 9 a^{4} : 3 a (2 a + 4 b - 3 a^{3})

= \frac{3 a ( 2 a + 4 b - 3 a ^{3} )}{3 a ^{3} b}

Cancel the common factor:

3

= \frac{a ( 2 a + 4 b - 3 a ^{3} )}{a ^{3} b}

Apply exponent rule:

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

a^{3} = a a^{2}

= \frac{a ( 2 a + 4 b - 3 a ^{3} )}{a a ^{2} b}

Cancel the common factor:

a

= \frac{2 a + 4 b - 3 a ^{3}}{a ^{2} b}

(4 x - 3)^{2} = 32

\frac{x + 3}{x - 2} \geq 0

3 (x - 2) + 4 = 2 (x + 3)

\frac{3}{4} \cdot 81.71

2 x^{2} - 6 x - 3 = 0

What is (6a^2+12ab-9a^4)/(3a^3b) ?
The solution to (6a^2+12ab-9a^4)/(3a^3b) is (2a+4b-3a^3)/(a^2b)