Simplify (3x^2y+15xy)/(x^2-25)

$\frac{3 x^{2} y + 15 x y}{x^{2} - 25}$

Step 1

Factor $3 x y$ out of $3 x^{2} y + 15 x y$ .

Factor $3 x y$ out of $3 x^{2} y$ .

$\frac{3 x y (x) + 15 x y}{x^{2} - 25}$

Factor $3 x y$ out of $15 x y$ .

$\frac{3 x y (x) + 3 x y (5)}{x^{2} - 25}$

Factor $3 x y$ out of $3 x y (x) + 3 x y (5)$ .

$\frac{3 x y (x + 5)}{x^{2} - 25}$

Step 2

Simplify the denominator.

Rewrite $25$ as $5^{2}$ .

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

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 $b = 5$ .

$\frac{3 x y (x + 5)}{(x + 5) (x - 5)}$

Step 3

Cancel the common factor of $x + 5$ .

Cancel the common factor.

$\frac{3 x y (x + 5)}{(x + 5) (x - 5)}$

Rewrite the expression.

$\frac{3 x y}{x - 5}$