x^2/(2-x)=2-4/(x-2)

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Solution for x^2/(2-x)=2-4/(x-2) equation: 


D( x )

2-x = 0

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

(x^2)/(2-x) = 2-(4/(x-2)) // - 2-(4/(x-2))

(x^2)/(2-x)+4/(x-2)-2 = 0

(x^2*(x-2))/((2-x)*(x-2))+(4*(2-x))/((2-x)*(x-2))+(-2*(2-x)*(x-2))/((2-x)*(x-2)) = 0

x^2*(x-2)+4*(2-x)-2*(2-x)*(x-2) = 0

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

x^3-12*x+16 = 0

x^3-12*x+16 = 0

x^3-12*x+16 = 0

{ 1, -1, 2, -2, 4, -4, 8, -8, 16, -16 }

1

x = 1

x^3-12*x+16 = 5

1

-1

x = -1

x^3-12*x+16 = 27

-1

2

x = 2

x^3-12*x+16 = 0

2

x-2

x^2+2*x-8

x^3-12*x+16

x-2

2*x^2-x^3

2*x^2-12*x+16

4*x-2*x^2

16-8*x

8*x-16

0

x^2+2*x-8 = 0

DELTA = 2^2-(-8*1*4)

DELTA = 36

DELTA > 0

x = (36^(1/2)-2)/(1*2) or x = (-36^(1/2)-2)/(1*2)

x = 2 or x = -4

x in { -4, 2, 2} 

(x+4)*(x-2)^2 = 0

((x+4)*(x-2)^2)/((2-x)*(x-2)) = 0

((x+4)*(x-2)^2)/((2-x)*(x-2)) = 0 // * (2-x)*(x-2)

(x+4)*(x-2)^2 = 0

( x+4 )

x+4 = 0 // - 4

x = -4

( x-2 )

x-2 = 0 // + 2

x = 2

x in { 2} 

x = -4

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