Basic Math Examples

$\frac{\frac{7 y}{y^{2} - 36}}{\frac{4 y - 20}{2 y + 12}}$

Step 1

Cancel the common factor of $4 y - 20$ and $2 y + 12$ .

Tap for more steps...

Step 1.1

Factor $2$ out of $4 y$ .

$\frac{\frac{7 y}{y^{2} - 36}}{\frac{2 (2 y) - 20}{2 y + 12}}$

Step 1.2

Factor $2$ out of $- 20$ .

$\frac{\frac{7 y}{y^{2} - 36}}{\frac{2 (2 y) + 2 \cdot - 10}{2 y + 12}}$

Step 1.3

Factor $2$ out of $2 (2 y) + 2 (- 10)$ .

$\frac{\frac{7 y}{y^{2} - 36}}{\frac{2 (2 y - 10)}{2 y + 12}}$

Step 1.4

Cancel the common factors.

Tap for more steps...

Step 1.4.1

Factor $2$ out of $2 y$ .

$\frac{\frac{7 y}{y^{2} - 36}}{\frac{2 (2 y - 10)}{2 (y) + 12}}$

Step 1.4.2

Factor $2$ out of $12$ .

$\frac{\frac{7 y}{y^{2} - 36}}{\frac{2 (2 y - 10)}{2 y + 2 \cdot 6}}$

Step 1.4.3

Factor $2$ out of $2 y + 2 \cdot 6$ .

$\frac{\frac{7 y}{y^{2} - 36}}{\frac{2 (2 y - 10)}{2 (y + 6)}}$

Step 1.4.4

Cancel the common factor.

$\frac{\frac{7 y}{y^{2} - 36}}{\frac{2 (2 y - 10)}{2 (y + 6)}}$

Step 1.4.5

Rewrite the expression.

$\frac{\frac{7 y}{y^{2} - 36}}{\frac{2 y - 10}{y + 6}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{7 y}{y^{2} - 36} \cdot \frac{y + 6}{2 y - 10}$

Step 3

Simplify the denominator.

Tap for more steps...

Step 3.1

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

$\frac{7 y}{y^{2} - 6^{2}} \cdot \frac{y + 6}{2 y - 10}$

Step 3.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = y$ and $b = 6$ .

$\frac{7 y}{(y + 6) (y - 6)} \cdot \frac{y + 6}{2 y - 10}$

Step 4

Simplify terms.

Tap for more steps...

Step 4.1

Cancel the common factor of $y + 6$ .

Tap for more steps...

Step 4.1.1

Cancel the common factor.

$\frac{7 y}{(y + 6) (y - 6)} \cdot \frac{y + 6}{2 y - 10}$

Step 4.1.2

Rewrite the expression.

$\frac{7 y}{y - 6} \cdot \frac{1}{2 y - 10}$

Step 4.2

Multiply $\frac{7 y}{y - 6}$ by $\frac{1}{2 y - 10}$ .

$\frac{7 y}{(y - 6) (2 y - 10)}$

Step 5

Factor $2$ out of $2 y - 10$ .

Tap for more steps...

Step 5.1

Factor $2$ out of $2 y$ .

$\frac{7 y}{(y - 6) (2 (y) - 10)}$

Step 5.2

Factor $2$ out of $- 10$ .

$\frac{7 y}{(y - 6) (2 y + 2 \cdot - 5)}$

Step 5.3

Factor $2$ out of $2 y + 2 \cdot - 5$ .

$\frac{7 y}{(y - 6) (2 (y - 5))}$

$\frac{7 y}{(y - 6) \cdot 2 (y - 5)}$

Step 6

Move $2$ to the left of $y - 6$ .

$\frac{7 y}{2 (y - 6) (y - 5)}$