(X)/(x+5)=(2x-8)/(x+8)

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Solution for (X)/(x+5)=(2x-8)/(x+8) equation: 


D( x )

x+5 = 0

x+8 = 0

x+5 = 0

x+5 = 0

x+5 = 0 // - 5

x = -5

x+8 = 0

x+8 = 0

x+8 = 0 // - 8

x = -8

x in (-oo:-8) U (-8:-5) U (-5:+oo)

X/(x+5) = (2*x-8)/(x+8) // - (2*x-8)/(x+8)

X/(x+5)-((2*x-8)/(x+8)) = 0

X/(x+5)+(-1*(2*x-8))/(x+8) = 0

(X*(x+8))/((x+5)*(x+8))+(-1*(2*x-8)*(x+5))/((x+5)*(x+8)) = 0

X*(x+8)-1*(2*x-8)*(x+5) = 0

X*x+8*X-2*x^2-2*x+40 = 0

(X*x+8*X-2*x^2-2*x+40)/((x+5)*(x+8)) = 0

(X*x+8*X-2*x^2-2*x+40)/((x+5)*(x+8)) = 0 // * (x+5)*(x+8)

X*x+8*X-2*x^2-2*x+40 = 0

8*X-2*x^2-2*x+40 = 0

DELTA = (-2)^2-(-2*4*(8*X+40))

DELTA = 8*(8*X+40)+4

8*(8*X+40)+4 = 0

8*(8*X+40)+4 = 0

64*X+324 = 0

64*X+324 = 0

64*X+324 = 0 // - 324

64*X = -324 // : 64

X = -324/64

X = -81/16

DELTA = 0  <=>  t_3 = -81/16

x = 2/(-2*2) i X = -81/16

x = -1/2 i X = -81/16

( x = ((8*(8*X+40)+4)^(1/2)+2)/(-2*2) or x = (2-(8*(8*X+40)+4)^(1/2))/(-2*2) ) i X > -81/16

( x = ((8*(8*X+40)+4)^(1/2)+2)/(-4) or x = (2-(8*(8*X+40)+4)^(1/2))/(-4) ) i X > -81/16

X+81/16 > 0

X+81/16 > 0 // - 81/16

X > -81/16

x in { -1/2, ((8*(8*X+40)+4)^(1/2)+2)/(-4), (2-(8*(8*X+40)+4)^(1/2))/(-4) }

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