X-1/x=x/x-2

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

X-1/X=X/X-2

We move all terms to the left:

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


Domain of the equation: X!=0

X∈R



Domain of the equation: X-2)!=0

X∈R


We get rid of parentheses

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

Fractions to decimals

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

3X+X*X-1=0

Wy multiply elements

X^2+3X-1=0

a = 1; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·1·(-1)
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{13}}{2*1}=\frac{-3-\sqrt{13}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{13}}{2*1}=\frac{-3+\sqrt{13}}{2}
$