(7x-1)/x-(3x)/(x+3)=4

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Solution for (7x-1)/x-(3x)/(x+3)=4 equation: 



(7x-1)/x-(3x)/(x+3)=4

We move all terms to the left:

(7x-1)/x-(3x)/(x+3)-(4)=0



Domain of the equation: x!=0

x∈R





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



We calculate fractions


(-3x^2)/(x^2+3x)+((7x-1)*(x+3))/(x^2+3x)-4=0



We calculate terms in parentheses: +((7x-1)*(x+3))/(x^2+3x), so:

(7x-1)*(x+3))/(x^2+3x

We add all the numbers together, and all the variables

3x+(7x-1)*(x+3))/(x^2

We multiply all the terms by the denominator


3x*(x^2+(7x-1)*(x+3))

Back to the equation:

+(3x*(x^2+(7x-1)*(x+3)))



We multiply all the terms by the denominator


(-3x^2)+((3x*(x^2+(7x-1)*(x+3))))*(x^2+3x)-4*(x^2+3x)=0



We calculate terms in parentheses: +((3x*(x^2+(7x-1)*(x+3))))*(x^2+3x), so:

(3x*(x^2+(7x-1)*(x+3))))*(x^2+3x

We add all the numbers together, and all the variables

3x+(3x*(x^2+(7x-1)*(x+3))))*(x^2

Back to the equation:

+(3x+(3x*(x^2+(7x-1)*(x+3))))*(x^2)



We multiply parentheses

(-3x^2)-4x^2+(3x+(3x*(x^2+(7x-1)*(x+3))))*x^2-12x=0

We get rid of parentheses

-3x^2-4x^2+(3x+(3x*(x^2+(7x-1)*(x+3))))*x^2-12x=0

We add all the numbers together, and all the variables

-7x^2-12x+(3x+(3x*(x^2+(7x-1)*(x+3))))*x^2=0

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