3/2y-1=2/y+2

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

3/2y-1=2/y+2

We move all terms to the left:

3/2y-1-(2/y+2)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



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

y∈R


We get rid of parentheses

3/2y-2/y-2-1=0

We calculate fractions


3y/2y^2+(-4y)/2y^2-2-1=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6y^2+3y+(-4y)=0

We get rid of parentheses

-6y^2+3y-4y=0

We add all the numbers together, and all the variables

-6y^2-1y=0

a = -6; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-6)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-6}=\frac{0}{-12}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-6}=\frac{2}{-12}
=-1/6
$