Algebra Examples

$\frac{2}{x + 1} - \frac{x}{x^{2} - 1}$

Step 1

Simplify the denominator.

Tap for more steps...

Step 1.1

Rewrite $1$ as $1^{2}$ .

$\frac{2}{x + 1} - \frac{x}{x^{2} - 1^{2}}$

Step 1.2

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 $b = 1$ .

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

Step 2

To write $\frac{2}{x + 1}$ as a fraction with a common denominator, multiply by $\frac{x - 1}{x - 1}$ .

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

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Multiply $\frac{2}{x + 1}$ by $\frac{x - 1}{x - 1}$ .

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

Step 3.2

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

Apply the distributive property.

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

Step 4.2

Multiply $2$ by $- 1$ .

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

Step 4.3

Subtract $x$ from $2 x$ .

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