# How do you do 5//2x-1 + 6x+7// 1-4x^2 ?

## Adding and Subtracting Expressions with Different Denominators.

##### 1 Answer

$= \frac{24 {x}^{2} + 4 x + 22}{4 {x}^{2} - 1}$

#### Explanation:

$\frac{5}{2 x - 1} + 6 x + \frac{7}{1 - 4 {x}^{2}} = \frac{5}{2 x - 1} + 6 x - \frac{7}{\left(1 - 2 x\right) \left(1 + 2 x\right)}$
$= \frac{5}{2 x - 1} + 6 x + \frac{7}{\left(2 x - 1\right) \left(2 x + 1\right)}$

The lcm is $\left(2 x + 1\right) \left(2 x - 1\right)$

$= \frac{5 \left(2 x + 1\right) + 6 x \left(2 x - 1\right) \left(2 x + 1\right) + 7 \left(1\right)}{\left(2 x - 1\right) \left(2 x + 1\right)}$

$= \frac{10 x + 15 + 6 x \left(4 {x}^{2} - 1\right) + 7}{4 {x}^{2} - 1}$

$\frac{= 10 x + 15 + 24 {x}^{2} - 6 x + 7}{4 {x}^{2} - 1}$

$= \frac{24 {x}^{2} + 4 x + 22}{4 {x}^{2} - 1}$
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