(4x^3-5x)/(2x-1)

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Solution for (4x^3-5x)/(2x-1) equation:


D( x )

2*x-1 = 0

2*x-1 = 0

2*x-1 = 0

2*x-1 = 0 // + 1

2*x = 1 // : 2

x = 1/2

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

(4*x^3-(5*x))/(2*x-1) = 0

(4*x^3-5*x)/(2*x-1) = 0

4*x^3-5*x = 0

x*(4*x^2-5) = 0

4*x^2 = 5 // : 4

x^2 = 5/4

x^2 = 5/4 // ^ 1/2

abs(x) = (5/4)^(1/2)

x = (5/4)^(1/2) or x = -(5/4)^(1/2)

x*(x-(5/4)^(1/2))*(x+(5/4)^(1/2)) = 0

(x*(x-(5/4)^(1/2))*(x+(5/4)^(1/2)))/(2*x-1) = 0

( x+(5/4)^(1/2) )

x+(5/4)^(1/2) = 0 // - (5/4)^(1/2)

x = -(5/4)^(1/2)

( x-(5/4)^(1/2) )

x-(5/4)^(1/2) = 0 // + (5/4)^(1/2)

x = (5/4)^(1/2)

( x )

x = 0

x in { -(5/4)^(1/2), (5/4)^(1/2), 0 }

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