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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x+3)!=0

x∈R


We add all the numbers together, and all the variables

x-3/x-(-1x-3/x+5)=0

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-5x+x*x+1x*x=0

Wy multiply elements

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

We add all the numbers together, and all the variables

2x^2-5x=0

a = 2; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·2·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*2}=\frac{10}{4}
=2+1/2
$