(x+3)/(x+4)-(x-5)/x=1

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Solution for (x+3)/(x+4)-(x-5)/x=1 equation: 



(x+3)/(x+4)-(x-5)/x=1

We move all terms to the left:

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



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

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

x!=-4

x∈R





Domain of the equation: x!=0

x∈R



We calculate fractions


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



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

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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


4x*(x^2-(x-5)*(x+4))

Back to the equation:

+(4x*(x^2-(x-5)*(x+4)))



We multiply all the terms by the denominator


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



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

(4x*(x^2-(x-5)*(x+4))))*(x^2+4x

We add all the numbers together, and all the variables

4x+(4x*(x^2-(x-5)*(x+4))))*(x^2

Back to the equation:

+(4x+(4x*(x^2-(x-5)*(x+4))))*(x^2)



We get rid of parentheses

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

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