# How do you simplify  (5y+3)/(y+2) - (2y-3)/(y+2)?

Mar 8, 2018

Combine the two fractions together since they both have the same denominator.

#### Explanation:

Let's use an easier example to illustrate this. $\frac{1}{2} + \frac{2}{2} = \frac{3}{2}$. This is done by combining the two fractions, which both have the same denominator (2 in this case). $\frac{1}{2} + \frac{2}{2} = \frac{1 + 2}{2} = \frac{3}{2}$

Let's use this to solve our problem:

$\frac{5 y + 3}{y + 2} - \frac{2 y - 3}{y + 2}$

$\frac{5 y + 3 - \left(2 y - 3\right)}{y + 2}$

$\frac{5 y + 3 - 2 y + 3}{y + 2}$

$\frac{3 y + 6}{y + 2}$

While we may seem like we're done, we haven't completely simplified our fraction. Let's factor out a 3 in the numerator to get our answer:

$\frac{3 \left(y + 2\right)}{y + 2}$

$3 \frac{\cancel{y + 2}}{\cancel{y + 2}} = 3$

Mar 8, 2018

$3$

#### Explanation:

$\frac{5 y + 3}{y + 2} - \frac{2 y - 3}{y + 2}$

$\therefore = \frac{\left(5 y + 3\right) - \left(2 y - 3\right)}{y + 2}$

$\therefore = \frac{5 y + 3 - 2 y + 3}{y + 2}$

$\therefore = \frac{3 y + 6}{y + 2}$

$\therefore = \frac{3 {\cancel{\left(y + 2\right)}}^{1}}{\cancel{y + 2}} ^ 1$

$\therefore = 3$