# Question #d9f0b

Feb 4, 2018

$\frac{2}{2 x + 11} - \frac{1}{x - 4} = \frac{1}{2}$

$\frac{2 \left(x - 4\right) - 1 \left(2 x + 11\right)}{\left(2 x + 11\right) \left(x - 4\right)} = \frac{1}{2}$

$\frac{2 x - 8 - 2 x - 11}{2 {x}^{2} + 11 x - 8 x - 44} = \frac{1}{2}$

$\frac{- 19}{2 {x}^{2} + 3 x - 44} = \frac{1}{2}$

$- 38 = 2 {x}^{2} + 3 x - 44$

$= 2 {x}^{2} + 3 x + 38 - 44$

$= 2 {x}^{2} + 3 x - 6$

Feb 4, 2018

Get rid of the denominators by multiplying through by the LCM.

Move all the terms to one side and simplify.

#### Explanation:

You need to get rid of the denominators in the given equation.
You can do this by multiplying each term by the LCM of the denominators, which is $\textcolor{b l u e}{2 \left(2 x + 11\right) \left(x - 4\right)}$..

Each denominator will cancel.

The left side will look like this:

$\frac{2 \times \textcolor{b l u e}{2 \cancel{\left(2 x + 11\right)} \left(x - 4\right)}}{\cancel{\left(2 x + 11\right)}} - \frac{1 \times \textcolor{b l u e}{2 \left(2 x + 11\right) \cancel{\left(x - 4\right)}}}{\cancel{\left(x - 4\right)}}$

and the right side like this: $\frac{1 \times \textcolor{b l u e}{\cancel{2} \left(2 x + 11\right) \left(x - 4\right)}}{\cancel{2}}$

This leaves the equation without fractions.

$4 \left(x - 4\right) - 2 \left(2 x + 11\right) = \left(2 x + 11\right) \left(x - 4\right)$

Multiply out the brackets:

$4 x - 16 - 4 x - 22 = 2 {x}^{2} + 3 x - 44$

Move all the terms to the right hand side.

$0 = 2 {x}^{2} + 3 x - 44 + 38$

$0 = 2 {x}^{2} + 3 x - 6$

This is the required equation.