Simplify 4/(x^2-25)-2/(x-5)

$\frac{4}{x^{2} - 25} - \frac{2}{x - 5}$

Step 1

Simplify the denominator.

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

$\frac{4}{x^{2} - 5^{2}} - \frac{2}{x - 5}$

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 $b = 5$ .

$\frac{4}{(x + 5) (x - 5)} - \frac{2}{x - 5}$

Step 2

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

$\frac{4}{(x + 5) (x - 5)} - \frac{2}{x - 5} \cdot \frac{x + 5}{x + 5}$

Step 3

Write each expression with a common denominator of $(x + 5) (x - 5)$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{4}{(x + 5) (x - 5)} - \frac{2 (x + 5)}{(x - 5) (x + 5)}$

Reorder the factors of $(x - 5) (x + 5)$ .

$\frac{4}{(x + 5) (x - 5)} - \frac{2 (x + 5)}{(x + 5) (x - 5)}$

Step 4

Combine the numerators over the common denominator.

$\frac{4 - 2 (x + 5)}{(x + 5) (x - 5)}$

Step 5

Simplify the numerator.

Factor $2$ out of $4 - 2 (x + 5)$ .

Factor $2$ out of $4$ .

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

Factor $2$ out of $- 2 (x + 5)$ .

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

Factor $2$ out of $2 (2) + 2 (- (x + 5))$ .

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

Apply the distributive property.

$\frac{2 (2 - x - 1 \cdot 5)}{(x + 5) (x - 5)}$

Multiply $- 1$ by $5$ .

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

Subtract $5$ from $2$ .

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

Step 6

Simplify with factoring out.

Factor $- 1$ out of $- x$ .

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

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{2 (- (x) - 1 (3))}{(x + 5) (x - 5)}$

Factor $- 1$ out of $- (x) - 1 (3)$ .

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

Simplify the expression.

Rewrite $- (x + 3)$ as $- 1 (x + 3)$ .

$\frac{2 (- 1 (x + 3))}{(x + 5) (x - 5)}$

Move the negative in front of the fraction.

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

Simplify 4/(x^2-25)-2/(x-5)

Related Questions

Support LCMGCF.com by disabling your adblocker.