X+2/x-1-2=3

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

X+2/X-1-2=3

We move all terms to the left:

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


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

X+2/X-6=0

We multiply all the terms by the denominator


X*X-6*X+2=0

We add all the numbers together, and all the variables

-6X+X*X+2=0

Wy multiply elements

X^2-6X+2=0

a = 1; b = -6; c = +2;
Δ = b2-4ac
Δ = -62-4·1·2
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{7}}{2*1}=\frac{6-2\sqrt{7}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{7}}{2*1}=\frac{6+2\sqrt{7}}{2}
$