2X-5/X-1=x-1/x=1

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

2X-5/X-1=X-1/X=1

We move all terms to the left:

2X-5/X-1-(X-1/X)=0


Domain of the equation: X!=0

X∈R



Domain of the equation: X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-1X+2X*X-X*X-4=0

Wy multiply elements

2X^2-1X^2-1X-4=0

We add all the numbers together, and all the variables

X^2-1X-4=0

a = 1; b = -1; c = -4;
Δ = b2-4ac
Δ = -12-4·1·(-4)
Δ = 17
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{-(-1)-\sqrt{17}}{2*1}=\frac{1-\sqrt{17}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{17}}{2*1}=\frac{1+\sqrt{17}}{2}
$