x/(x-6)-3=6/x-6

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Solution for x/(x-6)-3=6/x-6 equation: 



x/(x-6)-3=6/x-6

We move all terms to the left:

x/(x-6)-3-(6/x-6)=0



Domain of the equation: (x-6)!=0

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

x!=6

x∈R





Domain of the equation: x-6)!=0

x∈R



We get rid of parentheses

x/(x-6)-6/x+6-3=0

We calculate fractions


x^2/(x^2-6x)+(-6x+36)/(x^2-6x)+6-3=0

We add all the numbers together, and all the variables

x^2/(x^2-6x)+(-6x+36)/(x^2-6x)+3=0

We multiply all the terms by the denominator


x^2+(-6x+36)+3*(x^2-6x)=0

We multiply parentheses

x^2+3x^2+(-6x+36)-18x=0

We get rid of parentheses

x^2+3x^2-6x-18x+36=0

We add all the numbers together, and all the variables

4x^2-24x+36=0

a = 4; b = -24; c = +36;
Δ = b2-4ac
Δ = -242-4·4·36
Δ = 0
Delta is equal to zero, so there is only one solution to the equation

                              Stosujemy wzór:
$x=\frac{-b}{2a}=\frac{24}{8}=3$

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