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

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

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

We move all terms to the left:

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-3x+x*x=0

Wy multiply elements

x^2-3x=0

a = 1; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·1·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*1}=\frac{6}{2}
=3
$