Simplify (5/(2x+3y))÷(10/(4x^2-9y^2))

$\frac{5}{2 x + 3 y} \div \frac{10}{4 x^{2} - 9 y^{2}}$

To divide by a fraction, multiply by its reciprocal.

$\frac{5}{2 x + 3 y} \cdot \frac{4 x^{2} - 9 y^{2}}{10}$

Simplify terms.

Cancel the common factor of $5$ .

Factor $5$ out of $10$ .

$\frac{5}{2 x + 3 y} \cdot \frac{4 x^{2} - 9 y^{2}}{5 (2)}$

Cancel the common factor.

$\frac{5}{2 x + 3 y} \cdot \frac{4 x^{2} - 9 y^{2}}{5 \cdot 2}$

Rewrite the expression.

$\frac{1}{2 x + 3 y} \cdot \frac{4 x^{2} - 9 y^{2}}{2}$

Multiply $\frac{1}{2 x + 3 y}$ by $\frac{4 x^{2} - 9 y^{2}}{2}$ .

$\frac{4 x^{2} - 9 y^{2}}{(2 x + 3 y) \cdot 2}$

Simplify the numerator.

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

$\frac{{(2 x)}^{2} - 9 y^{2}}{(2 x + 3 y) \cdot 2}$

Rewrite $9 y^{2}$ as ${(3 y)}^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2 x$ and $b = 3 y$ .

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

Multiply $3$ by $- 1$ .

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

Cancel the common factor of $2 x + 3 y$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{2 x - 3 y}{2}$

Simplify (5/(2x+3y))÷(10/(4x^2-9y^2))

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