Simplify (4x)/(x-9)+3/2

$\frac{4 x}{x - 9} + \frac{3}{2}$

To write $\frac{4 x}{x - 9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{4 x}{x - 9} \cdot \frac{2}{2} + \frac{3}{2}$

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{x - 9}{x - 9}$ .

$\frac{4 x}{x - 9} \cdot \frac{2}{2} + \frac{3}{2} \cdot \frac{x - 9}{x - 9}$

Write each expression with a common denominator of $(x - 9) \cdot 2$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4 x}{x - 9}$ by $\frac{2}{2}$ .

$\frac{4 x \cdot 2}{(x - 9) \cdot 2} + \frac{3}{2} \cdot \frac{x - 9}{x - 9}$

Multiply $\frac{3}{2}$ by $\frac{x - 9}{x - 9}$ .

$\frac{4 x \cdot 2}{(x - 9) \cdot 2} + \frac{3 (x - 9)}{2 (x - 9)}$

Reorder the factors of $(x - 9) \cdot 2$ .

$\frac{4 x \cdot 2}{2 (x - 9)} + \frac{3 (x - 9)}{2 (x - 9)}$

Combine the numerators over the common denominator.

$\frac{4 x \cdot 2 + 3 (x - 9)}{2 (x - 9)}$

Simplify the numerator.

Multiply $2$ by $4$ .

$\frac{8 x + 3 (x - 9)}{2 (x - 9)}$

Apply the distributive property.

$\frac{8 x + 3 x + 3 \cdot - 9}{2 (x - 9)}$

Multiply $3$ by $- 9$ .

$\frac{8 x + 3 x - 27}{2 (x - 9)}$

Add $8 x$ and $3 x$ .

$\frac{11 x - 27}{2 (x - 9)}$