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

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

Step 1

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

Factor $3$ out of $3 x$ .

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

Factor $3$ out of $15$ .

$\frac{3 x + 3 \cdot 5}{x^{2} - 25}$

Factor $3$ out of $3 x + 3 \cdot 5$ .

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

Step 2

Simplify the denominator.

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

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

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 $b = 5$ .

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

Step 3

Cancel the common factor of $x + 5$ .

Cancel the common factor.

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

Rewrite the expression.

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