X-1=3/x+1

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

X-1=3/X+1

We move all terms to the left:

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


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

X∈R


We get rid of parentheses

X-3/X-1-1=0

We multiply all the terms by the denominator


X*X-1*X-1*X-3=0

We add all the numbers together, and all the variables

-2X+X*X-3=0

Wy multiply elements

X^2-2X-3=0

a = 1; b = -2; c = -3;
Δ = b2-4ac
Δ = -22-4·1·(-3)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4}{2*1}=\frac{-2}{2}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4}{2*1}=\frac{6}{2}
=3
$