# How do you simplify 3/(x+2) + 6/(x-1)?

Oct 9, 2015

By finding the Lowest Common Multiple (LCM)

Ans: $\frac{9 x + 9}{\left(x + 2\right) \left(x - 1\right)}$

#### Explanation:

$\frac{3}{x + 2} + \frac{6}{x - 1}$

Compare the denominators of $3$ and $6$.

Notice that the denominator of $3$ lacks $x - 1$, while the denominator of $6$ lacks $x + 2$.

Therefore, multiply $3$ by $x - 1$, and multiply $6$ by $x + 2$. Their sum will make up the numerator of your final expression.

To obtain the denominator of your final expression, multiply $x + 2$ by $x - 1$.

$\frac{3 \left(x - 1\right) + 6 \left(x + 2\right)}{\left(x + 2\right) \cdot \left(x - 1\right)}$

$\frac{3 x - 3 + 6 x + 12}{\left(x + 2\right) \left(x - 1\right)}$

$\frac{9 x + 9}{\left(x + 2\right) \left(x - 1\right)}$

The numerator and the denominator don't contain any common numbers that could be canceled out, so the expression can't be further simplified and this will be your final answer