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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

x-2/x-2x-1/x+1-5=0

We multiply all the terms by the denominator


x*x-2x*x+1*x-5*x-2-1=0

We add all the numbers together, and all the variables

-4x+x*x-2x*x-3=0

Wy multiply elements

x^2-2x^2-4x-3=0

We add all the numbers together, and all the variables

-1x^2-4x-3=0

a = -1; b = -4; c = -3;
Δ = b2-4ac
Δ = -42-4·(-1)·(-3)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2}{2*-1}=\frac{2}{-2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2}{2*-1}=\frac{6}{-2}
=-3
$