Divide (x^2-25)/(3x-15)

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

Step 1

Simplify the numerator.

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

$\frac{x^{2} - 5^{2}}{3 x - 15}$

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 $b = 5$ .

$\frac{(x + 5) (x - 5)}{3 x - 15}$

Step 2

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

Factor $3$ out of $3 x$ .

$\frac{(x + 5) (x - 5)}{3 (x) - 15}$

Factor $3$ out of $- 15$ .

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

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

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

Step 3

Cancel the common factor of $x - 5$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Split the fraction $\frac{x + 5}{3}$ into two fractions.

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