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

Solution for (2/y+1)-(3/1-y)=5/y equation:

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

We move all terms to the left:

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


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

y∈R



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

We move all terms containing y to the left, all other terms to the right

-y)!=-1

y!=-1/1

y!=-1

y∈R



Domain of the equation: y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


1y*y+1*y+2-5=0

We add all the numbers together, and all the variables

y+1y*y-3=0

Wy multiply elements

y^2+y-3=0

a = 1; b = 1; c = -3;
Δ = b2-4ac
Δ = 12-4·1·(-3)
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{13}}{2*1}=\frac{-1-\sqrt{13}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{13}}{2*1}=\frac{-1+\sqrt{13}}{2}
$