(X+4)/(x-4)+(x-2)/(x+-3)=19/3

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Solution for (X+4)/(x-4)+(x-2)/(x+-3)=19/3 equation: 



(X+4)/(X-4)+(X-2)/(X+-3)=19/3

We move all terms to the left:

(X+4)/(X-4)+(X-2)/(X+-3)-(19/3)=0



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





Domain of the equation: (X+-3)!=0

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

X+!=3

X∈R



We add all the numbers together, and all the variables

(X+4)/(X-4)+(X-2)/(X-3)-(+19/3)=0

We get rid of parentheses

(X+4)/(X-4)+(X-2)/(X-3)-19/3=0

We calculate fractions


((X+4)*(X-3)*3)/((X-4)*(X-3)*3)+((X-2)*(X-4)*3)/((X-4)*(X-3)*3)+(-19*(X-4)*(X-3))/((X-4)*(X-3)*3)=0



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

(X+4)*(X-3)*3)/((X-4)*(X-3)*3

We multiply all the terms by the denominator


(X+4)*(X-3)*3)

Back to the equation:

+((X+4)*(X-3)*3))





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

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

We multiply all the terms by the denominator


(X-2)*(X-4)*3)

Back to the equation:

+((X-2)*(X-4)*3))





We calculate terms in parentheses: +(-19*(X-4)*(X-3))/((X-4)*(X-3)*3), so:

-19*(X-4)*(X-3))/((X-4)*(X-3)*3

We multiply all the terms by the denominator


-19*(X-4)*(X-3))

Back to the equation:

+(-19*(X-4)*(X-3)))



We add all the numbers together, and all the variables

((X+4)*(X-3)*3))+((X-2)*(X-4)*3))+(-19*(X-4)*(X=0

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