Simplify 3/(x+1)+1/(x-1)

$\frac{3}{x + 1} + \frac{1}{x - 1}$

Step 1

To write $\frac{3}{x + 1}$ as a fraction with a common denominator, multiply by $\frac{x - 1}{x - 1}$ .

$\frac{3}{x + 1} \cdot \frac{x - 1}{x - 1} + \frac{1}{x - 1}$

Step 2

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

$\frac{3}{x + 1} \cdot \frac{x - 1}{x - 1} + \frac{1}{x - 1} \cdot \frac{x + 1}{x + 1}$

Step 3

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

Multiply $\frac{3}{x + 1}$ by $\frac{x - 1}{x - 1}$ .

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

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

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

Reorder the factors of $(x - 1) (x + 1)$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

Apply the distributive property.

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

Multiply $3$ by $- 1$ .

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

Add $3 x$ and $x$ .

$\frac{4 x - 3 + 1}{(x + 1) (x - 1)}$

Add $- 3$ and $1$ .

$\frac{4 x - 2}{(x + 1) (x - 1)}$

Factor $2$ out of $4 x - 2$ .

Factor $2$ out of $4 x$ .

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

Factor $2$ out of $- 2$ .

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

Factor $2$ out of $2 (2 x) + 2 (- 1)$ .

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