16=(2x)^2/(1-x)^2

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Solution for 16=(2x)^2/(1-x)^2 equation: 


D( x )

(1-x)^2 = 0

(1-x)^2 = 0

(1-x)^2 = 0

1-x = 0 // - 1

-x = -1 // * -1

x = 1

x in (-oo:1) U (1:+oo)

16 = ((2*x)^2)/((1-x)^2) // - ((2*x)^2)/((1-x)^2)

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

(-1*4*x^2)/((1-x)^2)+16 = 0

(-1*4*x^2)/((1-x)^2)+(16*(1-x)^2)/((1-x)^2) = 0

16*(1-x)^2-1*4*x^2 = 0

12*x^2-32*x+16 = 0

12*x^2-32*x+16 = 0

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

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

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

DELTA = 16

DELTA > 0

x = (16^(1/2)+8)/(2*3) or x = (8-16^(1/2))/(2*3)

x = 2 or x = 2/3

4*(x-2/3)*(x-2) = 0

(4*(x-2/3)*(x-2))/((1-x)^2) = 0

(4*(x-2/3)*(x-2))/((1-x)^2) = 0 // * (1-x)^2

4*(x-2/3)*(x-2) = 0

( x-2/3 )

x-2/3 = 0 // + 2/3

x = 2/3

( x-2 )

x-2 = 0 // + 2

x = 2

x in { 2/3, 2 }

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