Pre-Algebra Examples

$\frac{x}{x + 5} + \frac{3 x - 15}{x^{2} - 25}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

Factor $3$ out of $3 x$ .

$\frac{x}{x + 5} + \frac{3 (x) - 15}{x^{2} - 25}$

Step 1.1.2

Factor $3$ out of $- 15$ .

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

Step 1.1.3

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

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

Step 1.2

Simplify the denominator.

Tap for more steps...

Step 1.2.1

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

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

Step 1.2.2

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 $b = 5$ .

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

Step 1.3

Cancel the common factor of $x - 5$ .

Tap for more steps...

Step 1.3.1

Cancel the common factor.

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

Step 1.3.2

Rewrite the expression.

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

Step 2

Combine the numerators over the common denominator.

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