Simplify ((x^2-y^2)/y)÷((x+y)/(6y^2))

$\frac{x^{2} - y^{2}}{y} \div \frac{x + y}{6 y^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Simplify terms.

Cancel the common factor of $y$ .

Factor $y$ out of $6 y^{2}$ .

$\frac{x^{2} - y^{2}}{y} \cdot \frac{y (6 y)}{x + y}$

Cancel the common factor.

$\frac{x^{2} - y^{2}}{y} \cdot \frac{y (6 y)}{x + y}$

Rewrite the expression.

$(x^{2} - y^{2}) \frac{6 y}{x + y}$

Multiply $x^{2} - y^{2}$ by $\frac{6 y}{x + y}$ .

$\frac{(x^{2} - y^{2}) (6 y)}{x + y}$

Step 3

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 $b = y$ .

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

Step 4

Simplify terms.

Cancel the common factor of $x + y$ .

Cancel the common factor.

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

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

$(x - y) \cdot 6 y$

Apply the distributive property.

$(x \cdot 6 - y \cdot 6) y$

Simplify the expression.

Move $6$ to the left of $x$ .

$(6 \cdot x - y \cdot 6) y$

Multiply $6$ by $- 1$ .

$(6 \cdot x - 6 y) y$

Apply the distributive property.

$6 x y - 6 y \cdot y$

Step 5

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$6 x y - 6 (y \cdot y)$

Multiply $y$ by $y$ .

$6 x y - 6 y^{2}$