x/(2x+1)=5/(4-x)

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Solution for x/(2x+1)=5/(4-x) equation: 



x/(2x+1)=5/(4-x)

We move all terms to the left:

x/(2x+1)-(5/(4-x))=0



Domain of the equation: (2x+1)!=0

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

2x!=-1

x!=-1/2

x!=-1/2

x∈R





Domain of the equation: (4-x))!=0

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

-x)!=-4

x!=-4/1

x!=-4

x∈R



We add all the numbers together, and all the variables

x/(2x+1)-(5/(-1x+4))=0

We calculate fractions


3x^2/((2x+1)*(-1x+4)))+(-(5*(2x+1))/((2x+1)*(-1x+4)))=0



We calculate terms in parentheses: -(5*(2x+1))/((2x+1)*(-1x+4))), so:

5*(2x+1))/((2x+1)*(-1x+4))

We multiply all the terms by the denominator


5*(2x+1))

We multiply parentheses

10x+

We add all the numbers together, and all the variables

10x

Back to the equation:

-(10x)



We multiply all the terms by the denominator


3x^2-10x*((2x+1)*(-1x+4)))+(=0

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