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

Solution for (x+1)(x-1)/(x^2-1)=1/4 equation:

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

We move all terms to the left:

(x+1)(x-1)/(x^2-1)-(1/4)=0


Domain of the equation: (x^2-1)!=0

We move all terms containing x to the left, all other terms to the right

x^2!=1

x^2!=1/

x^2!=√1/

x!=1

x∈R


We add all the numbers together, and all the variables

(x+1)(x-1)/(x^2-1)-(+1/4)=0

We use the square of the difference formula

x^2-1-(+1/4)=0

We get rid of parentheses

x^2-1-1/4=0

We multiply all the terms by the denominator


x^2*4-1-1*4=0

We add all the numbers together, and all the variables

x^2*4-5=0

Wy multiply elements

4x^2-5=0

a = 4; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·4·(-5)
Δ = 80
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*4}=\frac{0-4\sqrt{5}}{8}
=-\frac{4\sqrt{5}}{8}
=-\frac{\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*4}=\frac{0+4\sqrt{5}}{8}
=\frac{4\sqrt{5}}{8}
=\frac{\sqrt{5}}{2}
$