How do you simplify $\frac{x + 1}{x - 1} = \frac{2}{2 x - 1} + \frac{2}{x - 1}$ $\frac { x + 1} { x - 1} = \frac { 2} { 2x - 1} + \frac { 2} { x - 1}$ ?

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How do you simplify $\frac{x + 1}{x - 1} = \frac{2}{2 x - 1} + \frac{2}{x - 1}$ $\frac { x + 1} { x - 1} = \frac { 2} { 2x - 1} + \frac { 2} { x - 1}$ ?

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Answer 1 · 2016-10-26T23:15:28

I found: $x = \frac{3}{2}$ $x=3/2$

Explanation:

Let us take $(x - 1) (2 x - 1)$ $(x-1)(2x-1)$ as common denominator and manipulate our fractions to get:

$\frac{(x + 1) (2 x - 1)}{(x - 1) (2 x - 1)} = \frac{2 (x - 1) + 2 (2 x - 1)}{(x - 1) (2 x - 1)}$ $((x+1)(2x-1))/((x-1)(2x-1))=(2(x-1)+2(2x-1))/((x-1)(2x-1))$

$(2x^2-x+2x-1)/cancel((x-1)(2x-1))=(2x-2+4x-2)/cancel((x-1)(2x-1))$

$2x^2-5x+3=0$

we use the Quadratic Formula:

$x_(1,2)=(5+-sqrt(25-24))/4$
$x_1=(5+1)/4=3/2$
$x_2=(5-1)/4=1$ that cannot be used because it will make the denominator $x-1$ equal to zero in the original expression!

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How do you simplify $\frac{x + 1}{x - 1} = \frac{2}{2 x - 1} + \frac{2}{x - 1}$ $\frac { x + 1} { x - 1} = \frac { 2} { 2x - 1} + \frac { 2} { x - 1}$ ?

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Explanation:

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Explanation:

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How do you simplify $\frac{x + 1}{x - 1} = \frac{2}{2 x - 1} + \frac{2}{x - 1}$ $\frac { x + 1} { x - 1} = \frac { 2} { 2x - 1} + \frac { 2} { x - 1}$ ?