Simplify 3/(2x)+5/(x-2)

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

To write $\frac{3}{2 x}$ as a fraction with a common denominator, multiply by $\frac{x - 2}{x - 2}$ .

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

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

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

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

Multiply $\frac{3}{2 x}$ by $\frac{x - 2}{x - 2}$ .

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

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

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

Reorder the factors of $(x - 2) (2 x)$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $3$ by $- 2$ .

$\frac{3 x - 6 + 5 \cdot 2 x}{2 x (x - 2)}$

Multiply $5$ by $2$ .

$\frac{3 x - 6 + 10 x}{2 x (x - 2)}$

Add $3 x$ and $10 x$ .

$\frac{13 x - 6}{2 x (x - 2)}$