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

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

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

We move all terms to the left:

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


Domain of the equation: y!=0

y∈R



Domain of the equation: y-5)!=0

y∈R


We get rid of parentheses

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

Fractions to decimals

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

4y-y*y-1=0

Wy multiply elements

-1y^2+4y-1=0

a = -1; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·(-1)·(-1)
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{3}}{2*-1}=\frac{-4-2\sqrt{3}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{3}}{2*-1}=\frac{-4+2\sqrt{3}}{-2}
$