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

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Solution for 5/(x+6)=2/(3-2x) equation:



5/(x+6)=2/(3-2x)
We move all terms to the left:
5/(x+6)-(2/(3-2x))=0
Domain of the equation: (x+6)!=0
We move all terms containing x to the left, all other terms to the right
x!=-6
x∈R
Domain of the equation: (3-2x))!=0
We move all terms containing x to the left, all other terms to the right
-2x)!=-3
x!=-3/1
x!=-3
x∈R
We add all the numbers together, and all the variables
5/(x+6)-(2/(-2x+3))=0
We calculate fractions
(-10x)/((x+6)*(-2x+3)))+(-(2*(x+6))/((x+6)*(-2x+3)))=0
We calculate terms in parentheses: -(2*(x+6))/((x+6)*(-2x+3))), so:
2*(x+6))/((x+6)*(-2x+3))
We multiply all the terms by the denominator
2*(x+6))
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+(-10x)/((x+6)*(-2x+3)))+(=0
We multiply all the terms by the denominator
-2x*((x+6)*(-2x+3)))+(+(-10x)=0
We get rid of parentheses
-2x*((x+6)*(-2x+3)))+(-10x=0
We add all the numbers together, and all the variables
-10x-2x*((x+6)*(-2x+3)))+(=0

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