What is (4-x^2)/(x^3-8) ?

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

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simplify (4-x^2)/(x^3-8)

simplify

\frac{4 - x ^{2}}{x ^{3} - 8}

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

Solution steps

\frac{4 - x ^{2}}{x ^{3} - 8}

Factor

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

= \frac{( 2 + x ) ( 2 - x )}{x ^{3} - 8}

Factor

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

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

(2 + x) (2 - x) = - (2 + x) (x - 2)

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

Cancel the common factor:

x - 2

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

Apply the fraction rule:

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

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

2300

(x + z)^{2}

\frac{2}{x - 3} + \frac{7}{3 - x}

e^{l n (7) - l n (2)}

\frac{- 12}{- 8}