(2/(x-1))=x+3

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

(2/(x-1))=x+3

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

(2/(x-1))-x-3=0

We multiply all the terms by the denominator


(2-x*(x-1))-3*(x-1))=0


We calculate terms in parentheses: +(2-x*(x-1)), so:

2-x*(x-1)

determiningTheFunctionDomain
-x*(x-1)+2

We multiply parentheses

-x^2+1x+2

We add all the numbers together, and all the variables

-1x^2+x+2

Back to the equation:

+(-1x^2+x+2)


We multiply parentheses

(-1x^2+x+2)-3x-=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2-2x=0

a = -1; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-1)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-1}=\frac{4}{-2}
=-2
$