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

Solution for 3(y+3)/y+1+2=3y+1/y+1 equation:

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

We move all terms to the left:

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


Domain of the equation: y!=0

y∈R



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

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


3(y+3)-3y*y-1*y+3*y-1=0

We add all the numbers together, and all the variables

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

We multiply parentheses

2y+3y-3y*y+9-1=0

Wy multiply elements

-3y^2+2y+3y+9-1=0

We add all the numbers together, and all the variables

-3y^2+5y+8=0

a = -3; b = 5; c = +8;
Δ = b2-4ac
Δ = 52-4·(-3)·8
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11}{2*-3}=\frac{-16}{-6}
=2+2/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*-3}=\frac{6}{-6}
=-1
$