y+3/2y+1-y-3/y+1=4

Solution for y+3/2y+1-y-3/y+1=4 equation:

y+3/2y+1-y-3/y+1=4

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-4y^2-3y=0

a = -4; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-4)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-4}=\frac{0}{-8}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-4}=\frac{6}{-8}
=-3/4
$