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

Dec 23, 2016

$\frac{x - 9}{3}$

#### Explanation:

To simplify this expression we need to add the fractions.

To add fractions we need to get each fraction over a common denominator, in this case $\textcolor{red}{6}$

To get each term over a common denominator we must multiply the fraction by the correct form of $1$:

$\left(\textcolor{b l u e}{\frac{3}{3}} \times \frac{x - 2}{2}\right) - \frac{x}{6} + \left(\textcolor{g r e e n}{\frac{6}{6}} \times - 2\right)$

$\frac{\textcolor{b l u e}{3} \times \left(x - 2\right)}{\textcolor{b l u e}{3} \times 2} - \frac{x}{6} + \frac{\textcolor{g r e e n}{6} \times - 2}{\textcolor{g r e e n}{6}}$

$\frac{3 x - 6}{6} - \frac{x}{6} + - \frac{12}{6}$

$\frac{3 x - 6}{6} - \frac{x}{6} - \frac{12}{6}$

We can now add the numerators to give:

$\frac{3 x - 6 - x - 12}{6}$

Next we can group like terms in the numerator:

$\frac{3 x - x - 6 - 12}{6}$

Then we can combine like terms in the numerator:

$\frac{\left(3 - 1\right) x - 18}{6}$

$\frac{\left(3 - 1\right) x - 18}{6}$

$\frac{2 x - 18}{6}$

Because 2, 18 and 6 are all divisible by $\textcolor{red}{2}$ we can still factor the terms:

$\frac{\textcolor{red}{2} \left(x - 9\right)}{\textcolor{red}{2} \times 3}$

$\frac{\textcolor{p u r p \le}{\cancel{\textcolor{red}{2}}} \left(x - 9\right)}{\textcolor{p u r p \le}{\cancel{\textcolor{red}{2}}} \times 3}$

$\frac{x - 9}{3}$