-x+k=1/(x-1)

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Solution for -x+k=1/(x-1) 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)

k-x = 1/(x-1) // - 1/(x-1)

k-(1/(x-1))-x = 0

k-(x-1)^-1-x = 0

k-1/(x-1)-x = 0

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

k*(x-1)-x*(x-1)-1 = 0

k*x-k-x^2+x-1 = 0

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

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

k*x-k-x^2+x-1 = 0

x-k-x^2-1 = 0

DELTA = 1^2-(-1*4*(-k-1))

DELTA = 1-4*(k+1)

1-4*(k+1) = 0

1-4*(k+1) = 0

-4*k-3 = 0

-4*k-3 = 0

-4*k-3 = 0 // + 3

-4*k = 3 // : -4

k = 3/(-4)

k = -3/4

DELTA = 0 <=> t_3 = -3/4

x = -1/(-1*2) i k = -3/4

x = 1/2 i k = -3/4

( x = ((1-4*(k+1))^(1/2)-1)/(-1*2) or x = (-(1-4*(k+1))^(1/2)-1)/(-1*2) ) i k > -3/4

( x = ((1-4*(k+1))^(1/2)-1)/(-2) or x = ((1-4*(k+1))^(1/2)+1)/2 ) i k > -3/4

k+3/4 > 0

k+3/4 > 0 // - 3/4

k > -3/4

x in { 1/2, ((1-4*(k+1))^(1/2)-1)/(-2), ((1-4*(k+1))^(1/2)+1)/2 }

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