(5x)/(x-2)=7+(10)/(x-2)

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Solution for (5x)/(x-2)=7+(10)/(x-2) equation: 


D( x )

x-2 = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x in (-oo:2) U (2:+oo)

(5*x)/(x-2) = 10/(x-2)+7 // - 10/(x-2)+7

(5*x)/(x-2)-(10/(x-2))-7 = 0

(5*x)/(x-2)-10*(x-2)^-1-7 = 0

(5*x)/(x-2)-10/(x-2)-7 = 0

(5*x)/(x-2)-10/(x-2)+(-7*(x-2))/(x-2) = 0

5*x-7*(x-2)-10 = 0

5*x-7*x-10+14 = 0

4-2*x = 0

(4-2*x)/(x-2) = 0

(4-2*x)/(x-2) = 0 // * x-2

4-2*x = 0

4-2*x = 0 // - 4

-2*x = -4 // : -2

x = -4/(-2)

x = 2

x in { 2} 

x belongs to the empty set

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