# How do you simplify  (x+1)/(3y) + (x-2)/(4y) - (x+3)/(6y) ?

Jul 9, 2018

$\frac{5 x - 8}{12 y}$

#### Explanation:

Since $12 y$ is the LCD of the denominators, that's what we want the denominator to be.

To achieve this, we can multiply the first fraction by $\frac{4}{4}$, the second by $\frac{3}{3}$, and the last by $\frac{2}{2}$. We now have

$\frac{4 \left(x + 1\right)}{12 y} + \frac{3 \left(x - 2\right)}{12 y} - \frac{2 \left(x + 3\right)}{12 y}$

This expression is equal to

$\frac{4 \left(x + 1\right) + 3 \left(x - 2\right) - 2 \left(x + 3\right)}{12 y}$

Let's distribute in the numerator to get

$\frac{4 x + 4 + 3 x - 6 - 2 x - 6}{12 y}$

In the numerator, we can combine like terms to get

$\frac{5 x - 8}{12 y}$

Since the terms have no common factors, we are done!

Hope this helps!