X=2y-3/y+1

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

X=2X-3/X+1

We move all terms to the left:

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


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

X∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

X^2-2X^2-1X+3=0

We add all the numbers together, and all the variables

-1X^2-1X+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:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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