# How do you simplify (x+1)/(x-1)=2/(2x-1)+2/(x-1)?

##### 2 Answers

$x = \frac{3}{2}$

#### Explanation:

Given that

$\setminus \frac{x + 1}{x - 1} = \setminus \frac{2}{2 x - 1} + \setminus \frac{2}{x - 1}$

$\setminus \frac{x + 1}{x - 1} - \setminus \frac{2}{2 x - 1} - \setminus \frac{2}{x - 1} = 0$

$\setminus \frac{\left(x + 1\right) \left(2 x - 1\right) - 2 \left(x - 1\right) - 2 \left(2 x - 1\right)}{\left(x - 1\right) \left(2 x - 1\right)} = 0$

$\setminus \frac{2 {x}^{2} - 5 x + 3}{\left(x - 1\right) \left(2 x - 1\right)} = 0$

$\setminus \frac{2 {x}^{2} - 2 x - 3 x + 3}{\left(x - 1\right) \left(2 x - 1\right)} = 0$

$\setminus \frac{2 x \left(x - 1\right) - 3 \left(x - 1\right)}{\left(x - 1\right) \left(2 x - 1\right)} = 0$

$\setminus \frac{\left(2 x - 3\right) \left(x - 1\right)}{\left(x - 1\right) \left(2 x - 1\right)} = 0$

$\setminus \frac{2 x - 3}{2 x - 1} = 0$

$2 x - 3 = 0 \setminus \quad \setminus \forall \setminus x \setminus \ne \frac{1}{2}$

$x = \frac{3}{2}$

Jun 26, 2018

$x = \frac{3}{2} \mathmr{and} 1.5$

#### Explanation:

we have
$\frac{x + 1}{x - 1} = \left(\frac{2}{2 x - 1}\right) + \left(\frac{2}{x - 1}\right)$
shifting $\left(\frac{2}{x - 1}\right)$ to other side
$\implies \frac{x + 1}{x - 1} - \left(\frac{2}{x - 1}\right) = \left(\frac{2}{2 x - 1}\right)$
$\implies \frac{x + 1 - 2}{x - 1} = \left(\frac{2}{2 x - 1}\right)$
$\implies \frac{\cancel{x - 1}}{\cancel{x - 1}} = \left(\frac{2}{2 x - 1}\right)$
=>2x-1=2; =>x=3/2 or 1.5