Divide ((y^2-16)/(4y-16))÷((y+4)/(16y))

$\frac{y^{2} - 16}{4 y - 16} \div \frac{y + 4}{16 y}$

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Simplify the numerator.

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

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

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 $b = 4$ .

$\frac{(y + 4) (y - 4)}{4 y - 16} \cdot \frac{16 y}{y + 4}$

Step 3

Factor $4$ out of $4 y - 16$ .

Factor $4$ out of $4 y$ .

$\frac{(y + 4) (y - 4)}{4 (y) - 16} \cdot \frac{16 y}{y + 4}$

Factor $4$ out of $- 16$ .

$\frac{(y + 4) (y - 4)}{4 y + 4 \cdot - 4} \cdot \frac{16 y}{y + 4}$

Factor $4$ out of $4 y + 4 \cdot - 4$ .

$\frac{(y + 4) (y - 4)}{4 (y - 4)} \cdot \frac{16 y}{y + 4}$

Step 4

Cancel the common factor of $y + 4$ .

Cancel the common factor.

$\frac{(y + 4) (y - 4)}{4 (y - 4)} \cdot \frac{16 y}{y + 4}$

Rewrite the expression.

$\frac{y - 4}{4 (y - 4)} (16 y)$

Step 5

Cancel the common factor of $4$ .

Factor $4$ out of $16 y$ .

$\frac{y - 4}{4 (y - 4)} (4 (4 y))$

Cancel the common factor.

$\frac{y - 4}{4 (y - 4)} (4 (4 y))$

Rewrite the expression.

$\frac{y - 4}{y - 4} (4 y)$

Step 6

Combine $4$ and $\frac{y - 4}{y - 4}$ .

$\frac{4 (y - 4)}{y - 4} y$

Step 7

Combine $\frac{4 (y - 4)}{y - 4}$ and $y$ .

$\frac{4 (y - 4) y}{y - 4}$

Step 8

Cancel the common factor of $y - 4$ .

Cancel the common factor.

$\frac{4 (y - 4) y}{y - 4}$

Divide $4 y$ by $1$ .

$4 y$