X/x+3-x+2/x-2=x+3/x-2

Solution for X/x+3-x+2/x-2=x+3/x-2 equation:

X/X+3-X+2/X-2=X+3/X-2

We move all terms to the left:

X/X+3-X+2/X-2-(X+3/X-2)=0


Domain of the equation: X!=0

X∈R



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

X∈R


We add all the numbers together, and all the variables

-1X+X/X+2/X-(X+3/X-2)+1=0

We get rid of parentheses

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

Fractions to decimals

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

4X-1X*X-X*X-1=0

Wy multiply elements

-1X^2-1X^2+4X-1=0

We add all the numbers together, and all the variables

-2X^2+4X-1=0

a = -2; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·(-2)·(-1)
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{-(4)-2\sqrt{2}}{2*-2}=\frac{-4-2\sqrt{2}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{2}}{2*-2}=\frac{-4+2\sqrt{2}}{-4}
$