(x+3)/(x-6)-(x+2)/(x-3)=2/5

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Solution for (x+3)/(x-6)-(x+2)/(x-3)=2/5 equation: 



(x+3)/(x-6)-(x+2)/(x-3)=2/5

We move all terms to the left:

(x+3)/(x-6)-(x+2)/(x-3)-(2/5)=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-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+3)/(x-6)-(x+2)/(x-3)-(+2/5)=0

We get rid of parentheses

(x+3)/(x-6)-(x+2)/(x-3)-2/5=0

We calculate fractions


((x+3)*(x-3)*5)/((x-6)*(x-3)*5)+(-(x+2)*(x-6)*5)/((x-6)*(x-3)*5)+(-2*(x-6)*(x-3))/((x-6)*(x-3)*5)=0



We calculate terms in parentheses: +((x+3)*(x-3)*5)/((x-6)*(x-3)*5), so:

(x+3)*(x-3)*5)/((x-6)*(x-3)*5

We multiply all the terms by the denominator


(x+3)*(x-3)*5)

Back to the equation:

+((x+3)*(x-3)*5))





We calculate terms in parentheses: +(-(x+2)*(x-6)*5)/((x-6)*(x-3)*5), so:

-(x+2)*(x-6)*5)/((x-6)*(x-3)*5

We multiply all the terms by the denominator


-(x+2)*(x-6)*5)

Back to the equation:

+(-(x+2)*(x-6)*5))





We calculate terms in parentheses: +(-2*(x-6)*(x-3))/((x-6)*(x-3)*5), so:

-2*(x-6)*(x-3))/((x-6)*(x-3)*5

We multiply all the terms by the denominator


-2*(x-6)*(x-3))

Back to the equation:

+(-2*(x-6)*(x-3)))



We add all the numbers together, and all the variables

((x+3)*(x-3)*5))+(-(x+2)*(x-6)*5))+(-2*(x-6)*(x=0

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