Precalculus Examples

$\frac{4 x - 16}{x^{2} - 8 x + 16}$

Step 1

Factor $4$ out of $4 x - 16$ .

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Step 1.1

Factor $4$ out of $4 x$ .

$\frac{4 (x) - 16}{x^{2} - 8 x + 16}$

Step 1.2

Factor $4$ out of $- 16$ .

$\frac{4 x + 4 \cdot - 4}{x^{2} - 8 x + 16}$

Step 1.3

Factor $4$ out of $4 x + 4 \cdot - 4$ .

$\frac{4 (x - 4)}{x^{2} - 8 x + 16}$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite $16$ as $4^{2}$ .

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

Step 2.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$8 x = 2 \cdot x \cdot 4$

Step 2.3

Rewrite the polynomial.

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

Step 2.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 4$ .

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

Step 3

Cancel the common factor of $x - 4$ and ${(x - 4)}^{2}$ .

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Step 3.1

Factor $x - 4$ out of $4 (x - 4)$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $x - 4$ out of ${(x - 4)}^{2}$ .

$\frac{(x - 4) \cdot 4}{(x - 4) (x - 4)}$

Step 3.2.2

Cancel the common factor.

$\frac{(x - 4) \cdot 4}{(x - 4) (x - 4)}$

Step 3.2.3

Rewrite the expression.

$\frac{4}{x - 4}$