Simplify (3x-5)/(x^2-25)-2/(x+5)

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

Step 1

Simplify the denominator.

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

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

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 $b = 5$ .

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

Step 2

To write $- \frac{2}{x + 5}$ as a fraction with a common denominator, multiply by $\frac{x - 5}{x - 5}$ .

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

Step 3

Simplify terms.

Multiply $\frac{2}{x + 5}$ by $\frac{x - 5}{x - 5}$ .

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

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

Apply the distributive property.

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

Multiply $- 2$ by $- 5$ .

$\frac{3 x - 5 - 2 x + 10}{(x + 5) (x - 5)}$

Subtract $2 x$ from $3 x$ .

$\frac{x - 5 + 10}{(x + 5) (x - 5)}$

Add $- 5$ and $10$ .

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

Step 5

Cancel the common factor of $x + 5$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{x - 5}$