2x-3/x+1+x-5/x-1=2

Solution for 2x-3/x+1+x-5/x-1=2 equation:

2x-3/x+1+x-5/x-1=2

We move all terms to the left:

2x-3/x+1+x-5/x-1-(2)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x-3/x-5/x-2=0

We multiply all the terms by the denominator


3x*x-2*x-3-5=0

We add all the numbers together, and all the variables

-2x+3x*x-8=0

Wy multiply elements

3x^2-2x-8=0

a = 3; b = -2; c = -8;
Δ = b2-4ac
Δ = -22-4·3·(-8)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10}{2*3}=\frac{-8}{6}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*3}=\frac{12}{6}
=2
$