X-1/x-2=3

Solution for X-1/x-2=3 equation:

X-1/X-2=3

We move all terms to the left:

X-1/X-2-(3)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

X-1/X-5=0

We multiply all the terms by the denominator


X*X-5*X-1=0

We add all the numbers together, and all the variables

-5X+X*X-1=0

Wy multiply elements

X^2-5X-1=0

a = 1; b = -5; c = -1;
Δ = b2-4ac
Δ = -52-4·1·(-1)
Δ = 29
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{-(-5)-\sqrt{29}}{2*1}=\frac{5-\sqrt{29}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{29}}{2*1}=\frac{5+\sqrt{29}}{2}
$