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

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



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

We move all terms to the left:

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



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

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

x!=2

x∈R





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

x∈R



We calculate fractions


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



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

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

We multiply all the terms by the denominator


2*(x-2))

We multiply parentheses

2x+

We add all the numbers together, and all the variables

2x

Back to the equation:

-(2x)



We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

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