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

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Solution for 1/(x-5)=x/(x^2-25) equation: 


D( x )

x-5 = 0

x^2-25 = 0

x-5 = 0

x-5 = 0

x-5 = 0 // + 5

x = 5

x^2-25 = 0

x^2-25 = 0

1*x^2 = 25 // : 1

x^2 = 25

x^2 = 25 // ^ 1/2

abs(x) = 5

x = 5 or x = -5

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

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

1/(x-5)-(x/(x^2-25)) = 0

1/(x-5)+(-1*x)/(x^2-25) = 0

(1*(x^2-25))/((x-5)*(x^2-25))+(-1*x*(x-5))/((x-5)*(x^2-25)) = 0

1*(x^2-25)-1*x*(x-5) = 0

5*x-25 = 0

(5*x-25)/((x-5)*(x^2-25)) = 0

(5*x-25)/((x-5)*(x^2-25)) = 0 // * (x-5)*(x^2-25)

5*x-25 = 0

5*x-25 = 0 // + 25

5*x = 25 // : 5

x = 25/5

x = 5

x in { 5} 

x belongs to the empty set

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