x/(x-5)=x/3

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


D( x )

x-5 = 0

x-5 = 0

x-5 = 0

x-5 = 0 // + 5

x = 5

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

x/(x-5) = x/3 // - x/3

x/(x-5)-(x/3) = 0

x/(x-5)-x/3 = 0

(3*x)/(3*(x-5))+(-x*(x-5))/(3*(x-5)) = 0

3*x-x*(x-5) = 0

8*x-x^2 = 0

8*x-x^2 = 0

x*(8-x) = 0

8-x = 0 // - 8

-x = -8 // * -1

x = 8

x*(x-8) = 0

(x*(x-8))/(3*(x-5)) = 0

(x*(x-8))/(3*(x-5)) = 0 // * 3*(x-5)

x*(x-8) = 0

( x-8 )

x-8 = 0 // + 8

x = 8

( x )

x = 0

x in { 8, 0 }

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