5/3y+5=1/y-1

Solution for 5/3y+5=1/y-1 equation:

5/3y+5=1/y-1

We move all terms to the left:

5/3y+5-(1/y-1)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



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

y∈R


We get rid of parentheses

5/3y-1/y+1+5=0

We calculate fractions


5y/3y^2+(-3y)/3y^2+1+5=0

We add all the numbers together, and all the variables

5y/3y^2+(-3y)/3y^2+6=0

We multiply all the terms by the denominator


5y+(-3y)+6*3y^2=0

Wy multiply elements

18y^2+5y+(-3y)=0

We get rid of parentheses

18y^2+5y-3y=0

We add all the numbers together, and all the variables

18y^2+2y=0

a = 18; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·18·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*18}=\frac{-4}{36}
=-1/9
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*18}=\frac{0}{36}
=0
$