What is (8-x^3)/(x^2+2x-8) ?

The solution to (8-x^3)/(x^2+2x-8) is -(x^2+2x+4)/(x+4)

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simplify (8-x^3)/(x^2+2x-8)

simplify

\frac{8 - x ^{3}}{x ^{2} + 2 x - 8}

- \frac{x ^{2} + 2 x + 4}{x + 4}

Solution steps

\frac{8 - x ^{3}}{x ^{2} + 2 x - 8}

Factor

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

= \frac{- ( x - 2 ) ( x ^{2} + 2 x + 4 )}{x ^{2} + 2 x - 8}

Factor

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

= \frac{- ( x - 2 ) ( x ^{2} + 2 x + 4 )}{( x - 2 ) ( x + 4 )}

Cancel the common factor:

x - 2

= \frac{- ( x ^{2} + 2 x + 4 )}{x + 4}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{x ^{2} + 2 x + 4}{x + 4}

2 \cdot 2^{\frac{3}{2}}

\frac{3}{4} \cdot \frac{1}{8}

\frac{272}{234}

\frac{x ^{2} - 5 x + 4}{x ^{2} - x - 12}

(15 - x)^{2}

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