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

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


D( x )

x^2+1 = 0

x^2+1 = 0

x^2+1 = 0

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

x^2 = -1

x in (-oo:+oo)

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

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

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

x^2+3*x-2 = 0

x^2+3*x-2 = 0

DELTA = 3^2-(-2*1*4)

DELTA = 17

DELTA > 0

x = (17^(1/2)-3)/(1*2) or x = (-17^(1/2)-3)/(1*2)

x = (17^(1/2)-3)/2 or x = (-(17^(1/2)+3))/2

(x+(17^(1/2)+3)/2)*(x-((17^(1/2)-3)/2)) = 0

((1-2*x^2)*(x+(17^(1/2)+3)/2)*(x-((17^(1/2)-3)/2)))/(x^2+1) = 0

( 1-2*x^2 )

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

x^2 = 1/2

x^2 = 1/2 // ^ 1/2

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

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

( x+(17^(1/2)+3)/2 )

x+(17^(1/2)+3)/2 = 0 // - (17^(1/2)+3)/2

x = -((17^(1/2)+3)/2)

( x-((17^(1/2)-3)/2) )

x-((17^(1/2)-3)/2) = 0 // + (17^(1/2)-3)/2

x = (17^(1/2)-3)/2

x in { (1/2)^(1/2), -(1/2)^(1/2), -((17^(1/2)+3)/2), (17^(1/2)-3)/2 }

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