Question

x+1/x-1-x-1/x+1=7/12​

Answer 1

Given:

The equation is:

$\dfrac{x+1}{x-1}-\dfrac{x-1}{x+1}=\dfrac{7}{12}$

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,

$\dfrac{x+1}{x-1}-\dfrac{x-1}{x+1}=\dfrac{7}{12}$

Taking LCM, we get

$\dfrac{(x+1)^2-(x^2-1)^2}{(x-1)(x+1)}=\dfrac{7}{12}$

$\dfrac{x^2+2x+1-(x^2-2x+1)}{x^2-1^2}=\dfrac{7}{12}$

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

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

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

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

$x=-\dfrac{1}{7},7$

Therefore, the values of x are $-\dfrac{1}{7}$ and $7$.