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

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

Step 1

Simplify the numerator.

Rewrite $8$ as $2^{3}$ .

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

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = x$ and $b = 2$ .

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

Simplify.

Move $2$ to the left of $x$ .

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

Raise $2$ to the power of $2$ .

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

Step 2

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 2$ .

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

Step 3

Cancel the common factor of $x - 2$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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