Z+1/z-2=z-1/z+3

Solution for Z+1/z-2=z-1/z+3 equation:

+1/Z-2=Z-1/Z+3

We move all terms to the left:

+1/Z-2-(Z-1/Z+3)=0


Domain of the equation: Z!=0

Z∈R



Domain of the equation: Z+3)!=0

Z∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-5Z-Z*Z+2=0

Wy multiply elements

-1Z^2-5Z+2=0

a = -1; b = -5; c = +2;
Δ = b2-4ac
Δ = -52-4·(-1)·2
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{33}}{2*-1}=\frac{5-\sqrt{33}}{-2}
$
$Z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{33}}{2*-1}=\frac{5+\sqrt{33}}{-2}
$