Simplify 5/(n+1)-3/(2(n-1))

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

To write $\frac{5}{n + 1}$ as a fraction with a common denominator, multiply by $\frac{2 (n - 1)}{2 (n - 1)}$ .

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

To write $- \frac{3}{2 (n - 1)}$ as a fraction with a common denominator, multiply by $\frac{n + 1}{n + 1}$ .

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

Write each expression with a common denominator of $(n + 1) \cdot 2 (n - 1)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{n + 1}$ by $\frac{2 (n - 1)}{2 (n - 1)}$ .

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

Multiply $\frac{3}{2 (n - 1)}$ by $\frac{n + 1}{n + 1}$ .

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

Reorder the factors of $(n + 1) (2 (n - 1))$ .

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

Reorder the factors of $2 (n - 1) (n + 1)$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $5$ by $2$ .

$\frac{10 (n - 1) - 3 (n + 1)}{2 (n + 1) (n - 1)}$

Apply the distributive property.

$\frac{10 n + 10 \cdot - 1 - 3 (n + 1)}{2 (n + 1) (n - 1)}$

Multiply $10$ by $- 1$ .

$\frac{10 n - 10 - 3 (n + 1)}{2 (n + 1) (n - 1)}$

Apply the distributive property.

$\frac{10 n - 10 - 3 n - 3 \cdot 1}{2 (n + 1) (n - 1)}$

Multiply $- 3$ by $1$ .

$\frac{10 n - 10 - 3 n - 3}{2 (n + 1) (n - 1)}$

Subtract $3 n$ from $10 n$ .

$\frac{7 n - 10 - 3}{2 (n + 1) (n - 1)}$

Subtract $3$ from $- 10$ .

$\frac{7 n - 13}{2 (n + 1) (n - 1)}$