x/x-2-2x+3/x-3=3-x^2/x^2-5x+6

Solution for x/x-2-2x+3/x-3=3-x^2/x^2-5x+6 equation:

x/x-2-2x+3/x-3=3-x^2/x^2-5x+6

We move all terms to the left:

x/x-2-2x+3/x-3-(3-x^2/x^2-5x+6)=0


Domain of the equation: x^2-5x+6)!=0

x∈R



Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-(3-x^2/x^2-5x+6)-2x+x/x+3/x-5=0

We get rid of parentheses

x^2/x^2+5x-2x+x/x+3/x-3-6-5=0

Fractions to decimals

3/x+5x-2x-3-6-5+1+1=0

We multiply all the terms by the denominator


5x*x-2x*x-3*x-6*x-5*x+1*x+1*x+3=0

We add all the numbers together, and all the variables

-12x+5x*x-2x*x+3=0

Wy multiply elements

5x^2-2x^2-12x+3=0

We add all the numbers together, and all the variables

3x^2-12x+3=0

a = 3; b = -12; c = +3;
Δ = b2-4ac
Δ = -122-4·3·3
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{3}}{2*3}=\frac{12-6\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{3}}{2*3}=\frac{12+6\sqrt{3}}{6}
$