Simplify (x^2+4xy)/(x^2-16y^2)

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

Step 1

Factor $x$ out of $x^{2} + 4 x y$ .

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

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

Factor $x$ out of $4 x y$ .

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

Factor $x$ out of $x \cdot x + x (4 y)$ .

$\frac{x (x + 4 y)}{x^{2} - 16 y^{2}}$

Step 2

Simplify the denominator.

Rewrite $16 y^{2}$ as ${(4 y)}^{2}$ .

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

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 $b = 4 y$ .

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

Multiply $4$ by $- 1$ .

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

Step 3

Cancel the common factor of $x + 4 y$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{x}{x - 4 y}$