X-2/x-1=1

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

X-2/X-1=1

We move all terms to the left:

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


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

X-2/X-2=0

We multiply all the terms by the denominator


X*X-2*X-2=0

We add all the numbers together, and all the variables

-2X+X*X-2=0

Wy multiply elements

X^2-2X-2=0

a = 1; b = -2; c = -2;
Δ = b2-4ac
Δ = -22-4·1·(-2)
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{3}}{2*1}=\frac{2-2\sqrt{3}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{3}}{2*1}=\frac{2+2\sqrt{3}}{2}
$