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

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


D( x )

x^2-2 = 0

x^2-2 = 0

x^2-2 = 0

1*x^2 = 2 // : 1

x^2 = 2

x^2 = 2 // ^ 1/2

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

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

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

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

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

4*x^2-4*x-1 = 0

4*x^2-4*x-1 = 0

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

DELTA = 32

DELTA > 0

x = (32^(1/2)+4)/(2*4) or x = (4-32^(1/2))/(2*4)

x = (4*2^(1/2)+4)/8 or x = (4-4*2^(1/2))/8

(x-((4-4*2^(1/2))/8))*(x-((4*2^(1/2)+4)/8)) = 0

((x-((4-4*2^(1/2))/8))*(x-((4*2^(1/2)+4)/8)))/(x^2-2) = 0

( x-((4*2^(1/2)+4)/8) )

x-((4*2^(1/2)+4)/8) = 0 // + (4*2^(1/2)+4)/8

x = (4*2^(1/2)+4)/8

( x-((4-4*2^(1/2))/8) )

x-((4-4*2^(1/2))/8) = 0 // + (4-4*2^(1/2))/8

x = (4-4*2^(1/2))/8

x in { (4*2^(1/2)+4)/8, (4-4*2^(1/2))/8 }

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