2-1/y-2=y-3/y-2

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

2-1/y-2=y-3/y-2

We move all terms to the left:

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


Domain of the equation: y!=0

y∈R



Domain of the equation: y-2)!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

2y-y*y+2=0

Wy multiply elements

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

a = -1; b = 2; c = +2;
Δ = b2-4ac
Δ = 22-4·(-1)·2
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{-(2)-2\sqrt{3}}{2*-1}=\frac{-2-2\sqrt{3}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{3}}{2*-1}=\frac{-2+2\sqrt{3}}{-2}
$