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

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Solution for ((x^2+2*x-1)/(2*x^2-3*x-2))^1/x equation: 


D( x )

2*x^2-(3*x)-2 = 0

x = 0

2*x^2-(3*x)-2 = 0

2*x^2-(3*x)-2 = 0

2*x^2-3*x-2 = 0

2*x^2-3*x-2 = 0

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

DELTA = 25

DELTA > 0

x = (25^(1/2)+3)/(2*2) or x = (3-25^(1/2))/(2*2)

x = 2 or x = -1/2

x = 0

x = 0

x in (-oo:-1/2) U (-1/2:0) U (0:2) U (2:+oo)

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

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

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

x^2+2*x-1 = 0

x^2+2*x-1 = 0

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

DELTA = 8

DELTA > 0

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

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

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

2*x^2-3*x-2 = 0

2*x^2-3*x-2 = 0

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

DELTA = 25

DELTA > 0

x = (25^(1/2)+3)/(2*2) or x = (3-25^(1/2))/(2*2)

x = 2 or x = -1/2

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

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

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

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

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

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

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

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

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

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