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

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

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

simplify

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

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

Solution steps

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

Factor

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

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

Factor

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

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

Cancel the common factor:

x - 2

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

4 - (- 6)

(x - 2)^{2} + 1

(\frac{a}{a ^{2}})^{- 2}

- 5 + (- 4)

(7 + m) (m - 7)