Algebra Examples

$\frac{x^{2} - 36}{6 - x}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $36$ as $6^{2}$ .

$\frac{x^{2} - 6^{2}}{6 - x}$

Step 1.2

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 $b = 6$ .

$\frac{(x + 6) (x - 6)}{6 - x}$

Step 2

Cancel the common factor of $x - 6$ and $6 - x$ .

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Step 2.1

Factor $- 1$ out of $x$ .

$\frac{(x + 6) (- 1 (- x) - 6)}{6 - x}$

Step 2.2

Rewrite $- 6$ as $- 1 (6)$ .

$\frac{(x + 6) (- 1 (- x) - 1 (6))}{6 - x}$

Step 2.3

Factor $- 1$ out of $- 1 (- x) - 1 (6)$ .

$\frac{(x + 6) (- 1 (- x + 6))}{6 - x}$

Step 2.4

Reorder terms.

$\frac{(x + 6) (- 1 (- x + 6))}{- x + 6}$

Step 2.5

Cancel the common factor.

$\frac{(x + 6) (- 1 (- x + 6))}{- x + 6}$

Step 2.6

Divide $(x + 6) \cdot (- 1)$ by $1$ .

$(x + 6) \cdot (- 1)$

Step 3

Apply the distributive property.

$x \cdot - 1 + 6 \cdot - 1$

Step 4

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

$- 1 \cdot x + 6 \cdot - 1$

Step 5

Multiply $6$ by $- 1$ .

$- 1 \cdot x - 6$

Step 6

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

$- x - 6$