# How can you evaluate (2)/(2x+1) + (4)/(x-2) ?

Jun 13, 2018

Put over a common denominator

#### Explanation:

I assume you mean "How can I put all of this over one fraction?"

Notice that multiplying by a fraction whose numerator and denominator are the same is multiplying by 1, changing nothing. Multiply each fraction by the other denominator in this fashion:

$\frac{2}{2 x + 1} + \frac{4}{x - 2} = \frac{2}{2 x + 1} \frac{x - 2}{x - 2} + \frac{4}{x - 2} \frac{2 x + 1}{2 x + 1}$
$= \frac{2 \left(x - 2\right) + 4 \left(2 x - 1\right)}{\left(2 x + 1\right) \left(x - 2\right)} = \frac{10 x - 8}{\left(2 x + 1\right) \left(x - 2\right)}$