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

Solution for x+2/x+3-x/x-1=0 equation:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+2/x-x/x+2=0

Fractions to decimals

2/x+x+2+1=0

We multiply all the terms by the denominator


x*x+2*x+1*x+2=0

We add all the numbers together, and all the variables

3x+x*x+2=0

Wy multiply elements

x^2+3x+2=0

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

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-1}{2*1}=\frac{-4}{2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+1}{2*1}=\frac{-2}{2}
=-1
$