x+2=1/x-1

Solution for x+2=1/x-1 equation:

x+2=1/x-1

We move all terms to the left:

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


Domain of the equation: x-1)!=0

x∈R


We get rid of parentheses

x-1/x+1+2=0

We multiply all the terms by the denominator


x*x+1*x+2*x-1=0

We add all the numbers together, and all the variables

3x+x*x-1=0

Wy multiply elements

x^2+3x-1=0

a = 1; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·1·(-1)
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{-(3)-\sqrt{13}}{2*1}=\frac{-3-\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{13}}{2*1}=\frac{-3+\sqrt{13}}{2}
$