# How do you simplify (18y)/(9y+2)-(-4)/(-2-9y)?

Feb 21, 2017

See the entire simplification process below:

#### Explanation:

First, multiply the second fraction in the expression by $\textcolor{red}{\frac{- 1}{-} 1}$ to put both fractions over a common denominator. We can multiply the fraction by this because it does not change the value of the fraction as $\frac{- 1}{-} 1 = 1$

$\frac{18 y}{9 y + 2} - \frac{- 4}{- 2 - 9 y}$ becomes:

$\frac{18 y}{9 y + 2} - \left(\textcolor{red}{\frac{- 1}{-} 1} \times \frac{- 4}{- 2 - 9 y}\right) \to$

$\frac{18 y}{9 y + 2} - \frac{- 1 \times - 4}{- 1 \left(- 2 - 9 y\right)} \to$

$\frac{18 y}{9 y + 2} - \frac{4}{2 + 9 y} \to$

$\frac{18 y}{9 y + 2} - \frac{4}{9 y + 2}$

We can now subtract the numerators of the two fractions because they have common denominators:

$\frac{18 y - 4}{9 y + 2}$