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

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



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

We move all terms to the left:

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



Domain of the equation: (2x-1)!=0

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

2x!=1

x!=1/2

x!=1/2

x∈R





Domain of the equation: (2x+1)!=0

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

2x!=-1

x!=-1/2

x!=-1/2

x∈R



We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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



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

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

We multiply all the terms by the denominator


(x+1)*(2x+1)*2)

Back to the equation:

+((x+1)*(2x+1)*2))





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

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

We multiply all the terms by the denominator


(x-1)*(2x-1)*2)

Back to the equation:

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





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

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

We multiply all the terms by the denominator


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

Back to the equation:

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



We add all the numbers together, and all the variables

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

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