(x-5)/(2x-6)+(x-7)/(12-4x)=x

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Solution for (x-5)/(2x-6)+(x-7)/(12-4x)=x equation: 



(x-5)/(2x-6)+(x-7)/(12-4x)=x

We move all terms to the left:

(x-5)/(2x-6)+(x-7)/(12-4x)-(x)=0



Domain of the equation: (2x-6)!=0

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

2x!=6

x!=6/2

x!=3

x∈R





Domain of the equation: (12-4x)!=0

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

-4x!=-12

x!=-12/-4

x!=+3

x∈R



We add all the numbers together, and all the variables

(x-5)/(2x-6)+(x-7)/(-4x+12)-x=0

We add all the numbers together, and all the variables

-1x+(x-5)/(2x-6)+(x-7)/(-4x+12)=0

We calculate fractions


-1x+((x-5)*(-4x+12))/((2x-6)*(-4x+12))+((x-7)*(2x-6))/((2x-6)*(-4x+12))=0



We calculate terms in parentheses: +((x-5)*(-4x+12))/((2x-6)*(-4x+12)), so:

(x-5)*(-4x+12))/((2x-6)*(-4x+12)

We multiply all the terms by the denominator


(x-5)*(-4x+12))

Back to the equation:

+((x-5)*(-4x+12)))





We calculate terms in parentheses: +((x-7)*(2x-6))/((2x-6)*(-4x+12)), so:

(x-7)*(2x-6))/((2x-6)*(-4x+12)

We multiply all the terms by the denominator


(x-7)*(2x-6))

Back to the equation:

+((x-7)*(2x-6)))





We calculate terms in parentheses: +((x-5)*(-4x+12)))+((x-7)*(2x-6))), so:

(x-5)*(-4x+12)))+((x-7)*(2x-6))

We add all the numbers together, and all the variables

(x-5)*(-4x+12)))+((x-7)*(2x

Back to the equation:

+((x-5)*(-4x+12)))+((x-7)*(2x)

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