Question

factorise 1/x-1 - 1/x+1 =6/7
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Answer 1

$\huge \purple {Answer}$

$\frac{1}{x - 1} - \frac{1}{x + 1} = \frac{6}{7}$

$\frac{x + 1 -( x - 1)}{(x - 1)(x + 1)} = \frac{6}{7}$

$\frac{x + 1 - x + 1}{ {x}^{2} - {1}^{2} } = \frac{6}{7}$

$\frac{2}{ {x}^{2} - 1} = \frac{6}{7}$

$2 = \frac{6 {x}^{2} - 6 }{7}$

$14 = 6 {x}^{2} - 6$

$14 + 6 = 6 {x}^{2}$

$20 = 6 {x}^{2}$

$\frac{20}{6} = {x}^{2}$

$\frac{10}{3} = {x}^{2}$

$x = \sqrt{ \frac{10}{3} }$

$\boxed {Hope \: it \: helps}$

Answer 2

Answer:

x = $\sqrt{10/3}$

Step-by-step explanation:

$1/(x-1) - 1/(x+1) = 6/7 ..........Given$

By taking LCM

$\frac{x+1-x+1}{(x-1)(x+1)} = \frac{6}{7}$

+1 and -1 cancel...

$\frac{2}{x^{2}+x-x-1 } = \frac{6}{7}$

+x and -x cancel.......

therefore, $\frac{2}{x^{2}-1} = \frac{6}{7}$

Then cross multiply.

$14 = 6x^{2} - 6$

$14+6 = 6x^{2} \\20 = 6x^{2}\\\frac{20}{6} = x^{2}\\\frac{10}{3} = x^{2} \\x = \sqrt{\frac{10}{3} }$

DONE...

Mark me the brainliest...