# How do you solve rational equations [(x+2) / (x-1)] = [1/2]?

Sep 16, 2016

$x = - 5$

#### Explanation:

When we have a fraction equal to another fraction we can use the method of $\textcolor{b l u e}{\text{cross-multiplication}}$ to solve.

That is $\frac{\textcolor{red}{x + 2}}{\textcolor{b l u e}{x - 1}} = \frac{\textcolor{b l u e}{1}}{\textcolor{red}{2}}$

Now multiply the terms on either end of an 'imaginary' cross (X). That is multiply the $\textcolor{red}{\text{red}}$ values together and the $\textcolor{b l u e}{\text{blue}}$ values together and equate them.

$\Rightarrow \textcolor{red}{2 \left(x + 2\right)} = \textcolor{b l u e}{1 \left(x - 1\right)}$

distribute the brackets.

$\Rightarrow 2 x + 4 = x - 1$

We now want to have the x terms on the left of the equation and numeric values on the right.

subtract x from both sides.

$2 x - x + 4 = \cancel{x} \cancel{- x} - 1$

$\Rightarrow x + 4 = - 1$

subtract 4 from both sides.

$x \cancel{+ 4} \cancel{- 4} = - 1 - 4$

$\Rightarrow x = - 5 \text{ is the solution}$