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

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


D( x )

(2*x-1)^2 = 0

(2*x-1)^2 = 0

(2*x-1)^2 = 0

2*x-1 = 0 // + 1

2*x = 1 // : 2

x = 1/2

x in (-oo:1/2) U (1/2:+oo)

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

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

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

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

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

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

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

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

4*x^3-4*x^2+x-1

4*x^3-1*(4*x^2+1)+x

x*(4*x^2+1)-1*(4*x^2+1)

(x-1)*(4*x^2+1)

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

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

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

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

( 2*x )

2*x = 0 // : 2

x = 0

( 4*x^2+1 )

4*x^2 = -1 // : 4

x^2 = -1/4

( x-1 )

x-1 = 0 // + 1

x = 1

x in { 0, 1 }

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