3x-3/x-1=2

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

3x-3/x-1=2

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x-3/x-3=0

We multiply all the terms by the denominator


3x*x-3*x-3=0

We add all the numbers together, and all the variables

-3x+3x*x-3=0

Wy multiply elements

3x^2-3x-3=0

a = 3; b = -3; c = -3;
Δ = b2-4ac
Δ = -32-4·3·(-3)
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{5}}{2*3}=\frac{3-3\sqrt{5}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{5}}{2*3}=\frac{3+3\sqrt{5}}{6}
$