x=4x-8/(x-4)(x+1)

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Solution for x=4x-8/(x-4)(x+1) equation:


D( x )

x-4 = 0

x-4 = 0

x-4 = 0

x-4 = 0 // + 4

x = 4

x in (-oo:4) U (4:+oo)

x = 4*x-((8/(x-4))*(x+1)) // - 4*x-((8/(x-4))*(x+1))

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

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

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

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

8*(x+1)+x*(x-4)-4*x*(x-4) = 0

x^2-4*x^2+4*x+16*x+8 = 0

20*x-3*x^2+8 = 0

20*x-3*x^2+8 = 0

20*x-3*x^2+8 = 0

DELTA = 20^2-(-3*4*8)

DELTA = 496

DELTA > 0

x = (496^(1/2)-20)/(-3*2) or x = (-496^(1/2)-20)/(-3*2)

x = (4*31^(1/2)-20)/(-6) or x = (-4*31^(1/2)-20)/(-6)

(x-((4*31^(1/2)-20)/(-6)))*(x-((-4*31^(1/2)-20)/(-6))) = 0

((x-((4*31^(1/2)-20)/(-6)))*(x-((-4*31^(1/2)-20)/(-6))))/(x-4) = 0

((x-((4*31^(1/2)-20)/(-6)))*(x-((-4*31^(1/2)-20)/(-6))))/(x-4) = 0 // * x-4

(x-((4*31^(1/2)-20)/(-6)))*(x-((-4*31^(1/2)-20)/(-6))) = 0

( x-((-4*31^(1/2)-20)/(-6)) )

x-((-4*31^(1/2)-20)/(-6)) = 0 // + (-4*31^(1/2)-20)/(-6)

x = (-4*31^(1/2)-20)/(-6)

( x-((4*31^(1/2)-20)/(-6)) )

x-((4*31^(1/2)-20)/(-6)) = 0 // + (4*31^(1/2)-20)/(-6)

x = (4*31^(1/2)-20)/(-6)

x in { (-4*31^(1/2)-20)/(-6), (4*31^(1/2)-20)/(-6) }

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