x-1/x-3=2

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

x-1/x-3=2

We move all terms to the left:

x-1/x-3-(2)=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}
$