How do you simplify 9+ (x-3)/ (x+2)?

Mar 27, 2018

The simplified expression is $\frac{10 x + 15}{x + 2}$.

Explanation:

Multiply $9$ by $\frac{x + 2}{x + 2}$ to get a common denominator, then combine the two fractions:

$\textcolor{w h i t e}{=} 9 + \frac{x - 3}{x + 2}$

$= 9 \textcolor{red}{\cdot \frac{\left(x + 2\right)}{x + 2}} + \frac{x - 3}{x + 2}$

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

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

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

$= \frac{\left(9 x + 18\right) + \left(x - 3\right)}{x + 2}$

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

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

$= \frac{10 x + 18 - 3}{x + 2}$

$= \frac{10 x + 15}{x + 2}$

That's it. Hope this helped!