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

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

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

We move all terms to the left:

2x-1/x-(3/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

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-2x+2x*x-4=0

Wy multiply elements

2x^2-2x-4=0

a = 2; b = -2; c = -4;
Δ = b2-4ac
Δ = -22-4·2·(-4)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6}{2*2}=\frac{-4}{4}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6}{2*2}=\frac{8}{4}
=2
$