(x-1)/(x-2)+(x-3)/(x-4)=10/3

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Solution for (x-1)/(x-2)+(x-3)/(x-4)=10/3 equation: 



(x-1)/(x-2)+(x-3)/(x-4)=10/3

We move all terms to the left:

(x-1)/(x-2)+(x-3)/(x-4)-(10/3)=0



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

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

x!=2

x∈R





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

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

x!=4

x∈R



We add all the numbers together, and all the variables

(x-1)/(x-2)+(x-3)/(x-4)-(+10/3)=0

We get rid of parentheses

(x-1)/(x-2)+(x-3)/(x-4)-10/3=0

We calculate fractions


((x-1)*(x-4)*3)/((x-2)*(x-4)*3)+((x-3)*(x-2)*3)/((x-2)*(x-4)*3)+(-10*(x-2)*(x-4))/((x-2)*(x-4)*3)=0



We calculate terms in parentheses: +((x-1)*(x-4)*3)/((x-2)*(x-4)*3), so:

(x-1)*(x-4)*3)/((x-2)*(x-4)*3

We multiply all the terms by the denominator


(x-1)*(x-4)*3)

Back to the equation:

+((x-1)*(x-4)*3))





We calculate terms in parentheses: +((x-3)*(x-2)*3)/((x-2)*(x-4)*3), so:

(x-3)*(x-2)*3)/((x-2)*(x-4)*3

We multiply all the terms by the denominator


(x-3)*(x-2)*3)

Back to the equation:

+((x-3)*(x-2)*3))





We calculate terms in parentheses: +(-10*(x-2)*(x-4))/((x-2)*(x-4)*3), so:

-10*(x-2)*(x-4))/((x-2)*(x-4)*3

We multiply all the terms by the denominator


-10*(x-2)*(x-4))

Back to the equation:

+(-10*(x-2)*(x-4)))



We add all the numbers together, and all the variables

((x-1)*(x-4)*3))+((x-3)*(x-2)*3))+(-10*(x-2)*(x=0

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