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

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Solution for (10/(x-5))+x=1+(2x/(x-5)) 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)

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

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

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

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

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

x*(x-5)-1*(x-5)-2*x+10 = 0

x^2-2*x-5*x-x+5+10 = 0

x^2-7*x-x+5+10 = 0

x^2-8*x+15 = 0

x^2-8*x+15 = 0

x^2-8*x+15 = 0

DELTA = (-8)^2-(1*4*15)

DELTA = 4

DELTA > 0

x = (4^(1/2)+8)/(1*2) or x = (8-4^(1/2))/(1*2)

x = 5 or x = 3

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

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

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

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

( x-3 )

x-3 = 0 // + 3

x = 3

( x-5 )

x-5 = 0 // + 5

x = 5

x in { 5} 

x = 3

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