Question

Solve for x x + 1 by x minus 1 minus x minus one by x + 1 is equal to 5 by 6

Answer 1

please write in proper form

• can't understand

Answer 2

Given: $\dfrac{x+1}{x-1}- \dfrac{x-1}{x+1} =\dfrac{5}{6}$

To find: The value of x

Step-by-step explanation:

As we have

$\dfrac{x+1}{x-1} -\dfrac{x-1}{x+1} =\dfrac{5}{6}$

So

$\dfrac{(x+1)^2-(x-1)^2}{(x+1)(x-1)} =\dfrac{5}{6}$

Now as we know

$a^2-b^2=(a+b)(a-b)$  we get

$\dfrac{(x+1+x-1)(x+1-(x-1)}{x^2-1} =\dfrac{5}{6} \\\\\Rightarrow \dfrac{2x \times 2}{x^2-1} =\dfrac{5}{6}\\\\\Rightarrow 6(4x)=5(x^2-1)\\\\\Rightarrow 24x=5x^2-5\\\\\Rightarrow 5x^2-24x-5=0\\\\\Rightarrow 5x^2-25x+x-5=0\\\\\Rightarrow 5x(x-5)+1(x-5)=0\\\\\Rightarrow (5x+1)(x-5)=0$

Therefore either

$5x+1=0 \text { or } (x-5)=0 \\\\\therefore x= \dfrac{-1}{5} \text { or } x=5$

Hence, the value of x are  $5 , \dfrac{-1}{5}$