(x-2/x-1)-(x+4/2x+2)=0

Solution for (x-2/x-1)-(x+4/2x+2)=0 equation:

(x-2/x-1)-(x+4/2x+2)=0


Domain of the equation: x-1)!=0

x∈R



Domain of the equation: 2x+2)!=0

x∈R


We get rid of parentheses

x-2/x-x-4/2x-1-2=0

We calculate fractions


x-x+(-4x)/2x^2+(-4x)/2x^2-1-2=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


(-4x)+(-4x)-3*2x^2=0

Wy multiply elements

-6x^2+(-4x)+(-4x)=0

We get rid of parentheses

-6x^2-4x-4x=0

We add all the numbers together, and all the variables

-6x^2-8x=0

a = -6; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-6)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-6}=\frac{0}{-12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-6}=\frac{16}{-12}
=-1+1/3
$