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

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

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

We move all terms to the left:

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


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

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

x!=-3

x∈R



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

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

-x)!=-5

x!=-5/1

x!=-5

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


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


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

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

We multiply all the terms by the denominator


3*(x+3))

We multiply parentheses

3x+

We add all the numbers together, and all the variables

3x

Back to the equation:

-(3x)


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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