What is (7x^2+8x-12)/(2x^3+4x^2-8x-16) ?

The solution to (7x^2+8x-12)/(2x^3+4x^2-8x-16) is (7x-6)/(2(x+2)(x-2))

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simplify (7x^2+8x-12)/(2x^3+4x^2-8x-16)

simplify

\frac{7 x ^{2} + 8 x - 12}{2 x ^{3} + 4 x ^{2} - 8 x - 16}

\frac{7 x - 6}{2 ( x + 2 ) ( x - 2 )}

Solution steps

\frac{7 x ^{2} + 8 x - 12}{2 x ^{3} + 4 x ^{2} - 8 x - 16}

Factor

7 x^{2} + 8 x - 12 : (7 x - 6) (x + 2)

= \frac{( 7 x - 6 ) ( x + 2 )}{2 x ^{3} + 4 x ^{2} - 8 x - 16}

Factor

2 x^{3} + 4 x^{2} - 8 x - 16 : 2 (x + 2)^{2} (x - 2)

= \frac{( 7 x - 6 ) ( x + 2 )}{2 ( x + 2 ) ^{2} ( x - 2 )}

Apply exponent rule:

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

(x + 2)^{2} = (x + 2) (x + 2)

= \frac{( 7 x - 6 ) ( x + 2 )}{2 ( x + 2 ) ( x + 2 ) ( x - 2 )}

Cancel the common factor:

x + 2

= \frac{7 x - 6}{2 ( x + 2 ) ( x - 2 )}

\frac{5}{6} \div 3

\frac{19}{38}

\frac{x ^{3} + 15 x ^{2} + 54 x}{2 x ^{4} + 6 x ^{3} - 108 x ^{2}} \cdot \frac{6 x ^{2} - 42 x + 36}{x ^{2} + 5 x - 6}

\frac{- 5 t ^{5}}{( 5 t ^{- 5} ) ^{2}}

e^{i}

What is (7x^2+8x-12)/(2x^3+4x^2-8x-16) ?
The solution to (7x^2+8x-12)/(2x^3+4x^2-8x-16) is (7x-6)/(2(x+2)(x-2))