Question

X+1/x-1-x-1/x+1=7/12​

Answer 1

Given:

The equation is:

`(x+1)/(x-1)-(x-1)/(x+1)=(7)/(12)`

To find:

The value of x.

Solution:

Formulae used:

`(a+b)^2=a^2+2ab+b^2`

`(a-b)^2=a^2-2ab+b^2`

`(a-b)(a+b)=a^2-b^2`

We have,

`(x+1)/(x-1)-(x-1)/(x+1)=(7)/(12)`

Taking LCM, we get

`((x+1)^2-(x^2-1)^2)/((x-1)(x+1))=(7)/(12)`

`(x^2+2x+1-(x^2-2x+1))/(x^2-1^2)=(7)/(12)`

On cross multiplication, we get

`12(x^2+2x+1-x^2+2x-1)=7(x^2-1)`

`12(4x)=7x^2-7`

`48x=7x^2-7`

`0=7x^2-48x-7`

Splitting the middle term, we get

`7x^2-49x+x-7=0`

`7x(x-7)+1(x-7)=0`

`(7x+1)(x-7)=0`

`x=-(1)/(7),7`

Therefore, the values of x are
`-(1)/(7)` and
`7`.