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

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



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

We move all terms to the left:

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



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

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

2x!=-3

x!=-3/2

x!=-1+1/2

x∈R





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

x∈R



We calculate fractions


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



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

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

We multiply all the terms by the denominator


2*(2x+3))

We multiply parentheses

4x+

We add all the numbers together, and all the variables

4x

Back to the equation:

-(4x)



We add all the numbers together, and all the variables

-4x+5x/((2x+3)*(x-3)))+(=0

We multiply all the terms by the denominator


-4x*((2x+3)*(x-3)))+(+5x=0

We add all the numbers together, and all the variables

5x-4x*((2x+3)*(x-3)))+(=0

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