Y+1/y-1=y-1/y-2

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

+1/Y-1=Y-1/Y-2

We move all terms to the left:

+1/Y-1-(Y-1/Y-2)=0


Domain of the equation: Y!=0

Y∈R



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

Y∈R


We get rid of parentheses

1/Y-Y+1/Y+2-1=0

We multiply all the terms by the denominator


-Y*Y+2*Y-1*Y+1+1=0

We add all the numbers together, and all the variables

Y-Y*Y+2=0

Wy multiply elements

-1Y^2+Y+2=0

a = -1; b = 1; c = +2;
Δ = b2-4ac
Δ = 12-4·(-1)·2
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3}{2*-1}=\frac{-4}{-2}
=+2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3}{2*-1}=\frac{2}{-2}
=-1
$