(x+1)/(2-x)*(2-x)^2/(x-2)*2/x+1

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Solution for (x+1)/(2-x)*(2-x)^2/(x-2)*2/x+1 equation: 


D( x )

2-x = 0

x-2 = 0

x = 0

2-x = 0

2-x = 0

2-x = 0 // - 2

-x = -2 // * -1

x = 2

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x = 0

x = 0

x in (-oo:0) U (0:2) U (2:+oo)

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

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

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

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

x^3-2*x^2-4*x+8 = 0

x^3-2*x^2-4*x+8 = 0

x^3-2*x^2-4*x+8 = 0

{ 1, -1, 2, -2, 4, -4, 8, -8 }

1

x = 1

x^3-2*x^2-4*x+8 = 3

1

-1

x = -1

x^3-2*x^2-4*x+8 = 9

-1

2

x = 2

x^3-2*x^2-4*x+8 = 0

2

x-2

x^2-4

x^3-2*x^2-4*x+8

x-2

2*x^2-x^3

8-4*x

4*x-8

0

x^2-4 = 0

DELTA = 0^2-(-4*1*4)

DELTA = 16

DELTA > 0

x = (16^(1/2)+0)/(1*2) or x = (0-16^(1/2))/(1*2)

x = 2 or x = -2

x in { -2, 2, 2} 

(x+2)*(x-2)^2 = 0

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

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

(x+2)*(x-2)^2 = 0

( x+2 )

x+2 = 0 // - 2

x = -2

( x-2 )

x-2 = 0 // + 2

x = 2

x in { 2} 

x = -2

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