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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $2$ by $- 9$ .

$\frac{2 x + 3 + 2 x - 18}{x - 9}$

Add $2 x$ and $2 x$ .

$\frac{4 x + 3 - 18}{x - 9}$

Subtract $18$ from $3$ .

$\frac{4 x - 15}{x - 9}$