3/(x-1)+x=5

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Solution for 3/(x-1)+x=5 equation: 


D( x )

x-1 = 0

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

x in (-oo:1) U (1:+oo)

3/(x-1)+x = 5 // - 5

3/(x-1)+x-5 = 0

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

x*(x-1)-5*(x-1)+3 = 0

x^2-x-5*x+3+5 = 0

x^2-6*x+8 = 0

x^2-6*x+8 = 0

x^2-6*x+8 = 0

DELTA = (-6)^2-(1*4*8)

DELTA = 4

DELTA > 0

x = (4^(1/2)+6)/(1*2) or x = (6-4^(1/2))/(1*2)

x = 4 or x = 2

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

((x-2)*(x-4))/(x-1) = 0

((x-2)*(x-4))/(x-1) = 0 // * x-1

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

( x-2 )

x-2 = 0 // + 2

x = 2

( x-4 )

x-4 = 0 // + 4

x = 4

x in { 2, 4 }

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