Algebra Examples

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

Simplify the numerator.

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Step 2.1

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

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

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 $a = 4$ and $b = x$ .

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

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $4 - x$ and $x - 4$ .

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Step 3.1.1

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

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

Step 3.1.2

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

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

Step 3.1.3

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

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

Step 3.1.4

Reorder terms.

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

Step 3.1.5

Cancel the common factor.

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

Step 3.1.6

Divide $(4 + x) \cdot (- 1)$ by $1$ .

$(4 + x) \cdot (- 1)$

Step 3.2

Simplify by multiplying through.

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Step 3.2.1

Apply the distributive property.

$4 \cdot - 1 + x \cdot - 1$

Step 3.2.2

Simplify the expression.

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Step 3.2.2.1

Multiply $4$ by $- 1$ .

$- 4 + x \cdot - 1$

Step 3.2.2.2

Move $- 1$ to the left of $x$ .

$- 4 - 1 \cdot x$

Step 3.3

Rewrite $- 1 x$ as $- x$ .

$- 4 - x$