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

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

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

We move all terms to the left:

2x-5/x-2-2-(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

2x-5/x-(3/x+2)-4=0

We get rid of parentheses

2x-5/x-3/x-2-4=0

We multiply all the terms by the denominator


2x*x-2*x-4*x-5-3=0

We add all the numbers together, and all the variables

-6x+2x*x-8=0

Wy multiply elements

2x^2-6x-8=0

a = 2; b = -6; c = -8;
Δ = b2-4ac
Δ = -62-4·2·(-8)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-10}{2*2}=\frac{-4}{4}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+10}{2*2}=\frac{16}{4}
=4
$