(x^2+3)/(x-1)=6

Solution for (x^2+3)/(x-1)=6 equation:

(x^2+3)/(x-1)=6

We move all terms to the left:

(x^2+3)/(x-1)-(6)=0


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

We move all terms containing x to the left, all other terms to the right

x!=1

x∈R


We multiply all the terms by the denominator


(x^2+3)-6*(x-1)=0

We multiply parentheses

(x^2+3)-6x+6=0

We get rid of parentheses

x^2-6x+3+6=0

We add all the numbers together, and all the variables

x^2-6x+9=0

a = 1; b = -6; c = +9;
Δ = b2-4ac
Δ = -62-4·1·9
Δ = 0
Delta is equal to zero, so there is only one solution to the equation

                              Stosujemy wzór:
$x=\frac{-b}{2a}=\frac{6}{2}=3$