45/(x+3)=20/(10-x)

Solution for 45/(x+3)=20/(10-x) equation:

45/(x+3)=20/(10-x)

We move all terms to the left:

45/(x+3)-(20/(10-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: (10-x))!=0

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

-x)!=-10

x!=-10/1

x!=-10

x∈R


We add all the numbers together, and all the variables

45/(x+3)-(20/(-1x+10))=0

We calculate fractions


(-45x)/((x+3)*(-1x+10)))+(-(20*(x+3))/((x+3)*(-1x+10)))=0


We calculate terms in parentheses: -(20*(x+3))/((x+3)*(-1x+10))), so:

20*(x+3))/((x+3)*(-1x+10))

We multiply all the terms by the denominator


20*(x+3))

We multiply parentheses

20x+

We add all the numbers together, and all the variables

20x

Back to the equation:

-(20x)


We add all the numbers together, and all the variables

-20x+(-45x)/((x+3)*(-1x+10)))+(=0

We multiply all the terms by the denominator


-20x*((x+3)*(-1x+10)))+(+(-45x)=0

We get rid of parentheses

-20x*((x+3)*(-1x+10)))+(-45x=0

We add all the numbers together, and all the variables

-45x-20x*((x+3)*(-1x+10)))+(=0