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

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



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

We move all terms to the left:

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



Domain of the equation: (3x-2)!=0

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

3x!=2

x!=2/3

x!=2/3

x∈R





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

x∈R



We calculate fractions


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



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

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

We multiply all the terms by the denominator


2*(3x-2))

We multiply parentheses

6x+

We add all the numbers together, and all the variables

6x

Back to the equation:

-(6x)



We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

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