Simplify ((x+y)/6)÷((x^2-y^2)/3)

$\frac{x + y}{6} \div \frac{x^{2} - y^{2}}{3}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x + y}{6} \cdot \frac{3}{x^{2} - y^{2}}$

Step 2

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\frac{x + y}{3 (2)} \cdot \frac{3}{x^{2} - y^{2}}$

Cancel the common factor.

$\frac{x + y}{3 \cdot 2} \cdot \frac{3}{x^{2} - y^{2}}$

Rewrite the expression.

$\frac{x + y}{2} \cdot \frac{1}{x^{2} - y^{2}}$

Step 3

Multiply $\frac{x + y}{2}$ by $\frac{1}{x^{2} - y^{2}}$ .

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

Step 4

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 $b = y$ .

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

Step 5

Cancel the common factor of $x + y$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{2 (x - y)}$