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

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


D( x )

x+5 = 0

x = 0

x^2+5*x = 0

x+5 = 0

x+5 = 0

x+5 = 0 // - 5

x = -5

x = 0

x = 0

x^2+5*x = 0

x^2+5*x = 0

x^2+5*x = 0

DELTA = 5^2-(0*1*4)

DELTA = 25

DELTA > 0

x = (25^(1/2)-5)/(1*2) or x = (-25^(1/2)-5)/(1*2)

x = 0 or x = -5

x in (-oo:-5) U (-5:0) U (0:+oo)

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

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

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

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

x^2+5*x = 0

x^2+5*x = 0

x*(x+5) = 0

x+5 = 0 // - 5

x = -5

x*(x+5) = 0

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

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

2*x-1*(x+5)-2 = 0

2*x-x-5-2 = 0

x-7 = 0

(x-7)/(x*(x+5)) = 0

(x-7)/(x*(x+5)) = 0 // * x*(x+5)

x-7 = 0

x-7 = 0 // + 7

x = 7

x = 7

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