# How do you write 2-(8a+5x)/(3a)+(2a+7x)/(9a) as a single fraction?

Dec 27, 2016

$\frac{- 4 a - 8 x}{9 a}$

or

$\frac{- 4 \left(a + 2 x\right)}{9 a}$

#### Explanation:

To add two fractions we need to have the fractions over a common denominator, in this case $\textcolor{b l u e}{9 a}$.

Therefore we need to multiple the constant and first fraction by the appropriate form of $1$:

$\left(\frac{\textcolor{red}{9 a}}{\textcolor{b l u e}{9 a}} \cdot 2\right) - \left(\frac{\textcolor{red}{3}}{\textcolor{b l u e}{3}} \cdot \frac{8 a + 5 x}{3 a}\right) + \frac{2 a + 7 x}{9 a}$

$\frac{\textcolor{red}{18 a}}{\textcolor{b l u e}{9 a}} - \frac{\textcolor{red}{3} \left(8 a + 5 x\right)}{\textcolor{b l u e}{9 a}} + \frac{2 a + 7 x}{\textcolor{b l u e}{9 a}}$

We can now expand the terms within parenthesis for the second fraction:

$\frac{18 a}{\textcolor{b l u e}{9 a}} - \frac{24 a + 15 x}{\textcolor{b l u e}{9 a}} + \frac{2 a + 7 x}{\textcolor{b l u e}{9 a}}$

We then can combine the numerators over a single common denominator:

$\frac{18 a - 24 a - 15 x + 2 a + 7 x}{\textcolor{b l u e}{9 a}}$

Next we can group like terms:

$\frac{18 a - 24 a + 2 a - 15 x + 7 x}{9 a}$

Now we can combine like terms:

$\frac{\left(18 - 24 + 2\right) a + \left(- 15 + 7\right) x}{9 a}$

$\frac{- 4 a - 8 x}{9 a}$

or

$\frac{- 4 \left(a + 2 x\right)}{9 a}$