x-3/x-2=-1/x-2

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

x-3/x-2=-1/x-2

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x-2)!=0

x∈R


We get rid of parentheses

x-3/x+1/x+2-2=0

We multiply all the terms by the denominator


x*x+2*x-2*x-3+1=0

We add all the numbers together, and all the variables

x*x-2=0

Wy multiply elements

x^2-2=0

a = 1; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·1·(-2)
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2}}{2*1}=\frac{0-2\sqrt{2}}{2}
=-\frac{2\sqrt{2}}{2}
=-\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2}}{2*1}=\frac{0+2\sqrt{2}}{2}
=\frac{2\sqrt{2}}{2}
=\sqrt{2}
$