Simplify (3/(x+1)+2/(x-1))/((x-1)/(x+1))

$\frac{\frac{3}{x + 1} + \frac{2}{x - 1}}{\frac{x - 1}{x + 1}}$

Multiply the numerator by the reciprocal of the denominator.

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

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

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

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

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $3$ by $- 1$ .

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

Apply the distributive property.

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

Multiply $2$ by $1$ .

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

Add $3 x$ and $2 x$ .

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

Add $- 3$ and $2$ .

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

Simplify terms.

Cancel the common factor of $x + 1$ .

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $\frac{5 x - 1}{x - 1}$ by $\frac{1}{x - 1}$ .

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

Raise $x - 1$ to the power of $1$ .

$\frac{5 x - 1}{{(x - 1)}^{1} (x - 1)}$

Raise $x - 1$ to the power of $1$ .

$\frac{5 x - 1}{{(x - 1)}^{1} {(x - 1)}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $1$ .

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