Pre-Algebra Examples

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

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

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

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

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 $a = 6$ and $b = y$ .

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

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

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

Tap for more steps...

Step 2.1.1

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

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

Step 2.1.2

Factor $- 1$ out of $- y$ .

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

Step 2.1.3

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

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

Step 2.1.4

Reorder terms.

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

Step 2.1.5

Cancel the common factor.

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

Step 2.1.6

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

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

Step 2.2

Simplify by multiplying through.

Tap for more steps...

Step 2.2.1

Apply the distributive property.

$6 \cdot - 1 + y \cdot - 1$

Step 2.2.2

Simplify the expression.

Tap for more steps...

Step 2.2.2.1

Multiply $6$ by $- 1$ .

$- 6 + y \cdot - 1$

Step 2.2.2.2

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

$- 6 - 1 \cdot y$

Step 2.3

Rewrite $- 1 y$ as $- y$ .

$- 6 - y$