Pre-Algebra Examples

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

Step 1

Simplify terms.

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Step 1.1

Rewrite $4$ as $- 1 (- 4)$ .

$\frac{x^{2}}{x - 4} + \frac{16}{- 1 (- 4) - x}$

Step 1.2

Factor $- 1$ out of $- x$ .

$\frac{x^{2}}{x - 4} + \frac{16}{- 1 (- 4) - (x)}$

Step 1.3

Factor $- 1$ out of $- 1 (- 4) - (x)$ .

$\frac{x^{2}}{x - 4} + \frac{16}{- 1 (- 4 + x)}$

Step 1.4

Simplify the expression.

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Step 1.4.1

Move a negative from the denominator of $\frac{16}{- 1 (- 4 + x)}$ to the numerator.

$\frac{x^{2}}{x - 4} + \frac{- 1 \cdot 16}{- 4 + x}$

Step 1.4.2

Reorder terms.

$\frac{x^{2}}{x - 4} + \frac{- 1 \cdot 16}{x - 4}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{x^{2} - 1 \cdot 16}{x - 4}$

Step 2

Simplify the numerator.

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Step 2.1

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

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

Step 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 $b = 4$ .

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

Step 3

Cancel the common factor of $x - 4$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Divide $x + 4$ by $1$ .

$x + 4$