(x+1)/(x-1)-(2x+5)/(5x-2)=3/5

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Solution for (x+1)/(x-1)-(2x+5)/(5x-2)=3/5 equation: 



(x+1)/(x-1)-(2x+5)/(5x-2)=3/5

We move all terms to the left:

(x+1)/(x-1)-(2x+5)/(5x-2)-(3/5)=0



Domain of the equation: (x-1)!=0

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

x!=1

x∈R





Domain of the equation: (5x-2)!=0

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

5x!=2

x!=2/5

x!=2/5

x∈R



We add all the numbers together, and all the variables

(x+1)/(x-1)-(2x+5)/(5x-2)-(+3/5)=0

We get rid of parentheses

(x+1)/(x-1)-(2x+5)/(5x-2)-3/5=0

We calculate fractions


((x+1)*(5x-2)*5)/((x-1)*(5x-2)*5)+(-(2x+5)*(x-1)*5)/((x-1)*(5x-2)*5)+(-3*(x-1)*(5x-2))/((x-1)*(5x-2)*5)=0



We calculate terms in parentheses: +((x+1)*(5x-2)*5)/((x-1)*(5x-2)*5), so:

(x+1)*(5x-2)*5)/((x-1)*(5x-2)*5

We multiply all the terms by the denominator


(x+1)*(5x-2)*5)

Back to the equation:

+((x+1)*(5x-2)*5))





We calculate terms in parentheses: +(-(2x+5)*(x-1)*5)/((x-1)*(5x-2)*5), so:

-(2x+5)*(x-1)*5)/((x-1)*(5x-2)*5

We multiply all the terms by the denominator


-(2x+5)*(x-1)*5)

Back to the equation:

+(-(2x+5)*(x-1)*5))





We calculate terms in parentheses: +(-3*(x-1)*(5x-2))/((x-1)*(5x-2)*5), so:

-3*(x-1)*(5x-2))/((x-1)*(5x-2)*5

We multiply all the terms by the denominator


-3*(x-1)*(5x-2))

Back to the equation:

+(-3*(x-1)*(5x-2)))



We add all the numbers together, and all the variables

((x+1)*(5x-2)*5))+(-(2x+5)*(x-1)*5))+(-3*(x-1)*(5x=0

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