2/2x-5=3/x+1

Solution for 2/2x-5=3/x+1 equation:

2/2x-5=3/x+1

We move all terms to the left:

2/2x-5-(3/x+1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

2/2x-3/x-1-5=0

We calculate fractions


2x/2x^2+(-6x)/2x^2-1-5=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-12x^2+2x+(-6x)=0

We get rid of parentheses

-12x^2+2x-6x=0

We add all the numbers together, and all the variables

-12x^2-4x=0

a = -12; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-12)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-12}=\frac{0}{-24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-12}=\frac{8}{-24}
=-1/3
$