x-(10/(x-1))=4

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Solution for x-(10/(x-1))=4 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)

x-(10/(x-1)) = 4 // - 4

x-(10/(x-1))-4 = 0

x-10*(x-1)^-1-4 = 0

x-10/(x-1)-4 = 0

(x*(x-1))/(x-1)-10/(x-1)+(-4*(x-1))/(x-1) = 0

x*(x-1)-4*(x-1)-10 = 0

x^2-x-4*x-10+4 = 0

x^2-5*x-6 = 0

x^2-5*x-6 = 0

x^2-5*x-6 = 0

DELTA = (-5)^2-(-6*1*4)

DELTA = 49

DELTA > 0

x = (49^(1/2)+5)/(1*2) or x = (5-49^(1/2))/(1*2)

x = 6 or x = -1

(x+1)*(x-6) = 0

((x+1)*(x-6))/(x-1) = 0

((x+1)*(x-6))/(x-1) = 0 // * x-1

(x+1)*(x-6) = 0

( x+1 )

x+1 = 0 // - 1

x = -1

( x-6 )

x-6 = 0 // + 6

x = 6

x in { -1, 6 }

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