x-4/x-4=2/x-1

Solution for x-4/x-4=2/x-1 equation:

x-4/x-4=2/x-1

We move all terms to the left:

x-4/x-4-(2/x-1)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x-1)!=0

x∈R


We get rid of parentheses

x-4/x-2/x+1-4=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-3x+x*x-6=0

Wy multiply elements

x^2-3x-6=0

a = 1; b = -3; c = -6;
Δ = b2-4ac
Δ = -32-4·1·(-6)
Δ = 33
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{-(-3)-\sqrt{33}}{2*1}=\frac{3-\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{33}}{2*1}=\frac{3+\sqrt{33}}{2}
$