X/x-1=x-2/x+1

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

X/X-1=X-2/X+1

We move all terms to the left:

X/X-1-(X-2/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/X-X+2/X-1-1=0

Fractions to decimals

2/X-X-1-1+1=0

We multiply all the terms by the denominator


-X*X-1*X-1*X+1*X+2=0

We add all the numbers together, and all the variables

-1X-X*X+2=0

Wy multiply elements

-1X^2-1X+2=0

a = -1; b = -1; c = +2;
Δ = b2-4ac
Δ = -12-4·(-1)·2
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3}{2*-1}=\frac{-2}{-2}
=1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3}{2*-1}=\frac{4}{-2}
=-2
$