(x^2-6x+5/4(x^2-1))/(2x^2-11x-5/8x^2-4x)

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Solution for (x^2-6x+5/4(x^2-1))/(2x^2-11x-5/8x^2-4x) equation: 


D( x )

2*x^2-((5/8)*x^2)-(11*x)-(4*x) = 0

2*x^2-((5/8)*x^2)-(11*x)-(4*x) = 0

2*x^2-((5/8)*x^2)-(11*x)-(4*x) = 0

2*x^2+(-5/8)*x^2-11*x-4*x = 0

11/8*x^2-15*x = 0

DELTA = (-15)^2-(0*11/8*4)

DELTA = 225

DELTA > 0

x = (225^(1/2)+15)/(11/8*2) or x = (15-225^(1/2))/(11/8*2)

x = 120/11 or x = 0

x in (-oo:0) U (0:120/11) U (120/11:+oo)

((5/4)*(x^2-1)+x^2-(6*x))/(2*x^2-((5/8)*x^2)-(11*x)-(4*x)) = 0

((5/4)*(x^2-1)+x^2-6*x)/(2*x^2+(-5/8)*x^2-11*x-4*x) = 0

(5/4*(x^2-1)+x^2-6*x)/(11/8*x^2-15*x) = 0

11/8*x^2-15*x = 0

x*(11/8*x-15) = 0

11/8*x-15 = 0 // + 15

11/8*x = 15 // : 11/8

x = 15/11/8

x = 120/11

x*(x-120/11) = 0

5/4*(x^2-1)+x^2-6*x = 0

5/4*(x^2-1)+x^2-6*x = 0

9/4*x^2-6*x-5/4 = 0

9/4*x^2-6*x-5/4 = 0

9/4*x^2-6*x-5/4 = 0

DELTA = (-6)^2-(-5/4*9/4*4)

DELTA = 189/4

DELTA > 0

x = ((189/4)^(1/2)+6)/(2*9/4) or x = (6-(189/4)^(1/2))/(2*9/4)

x = 2/9*((189/4)^(1/2)+6) or x = 2/9*(6-(189/4)^(1/2))

(x-2/9*(6-(189/4)^(1/2)))*(x-2/9*((189/4)^(1/2)+6)) = 0

(x-2/9*(6-(189/4)^(1/2)))*(x-2/9*((189/4)^(1/2)+6)) = 0

((x-2/9*(6-(189/4)^(1/2)))*(x-2/9*((189/4)^(1/2)+6)))/(x*(x-120/11)) = 0

( x-2/9*((189/4)^(1/2)+6) )

x-2/9*((189/4)^(1/2)+6) = 0 // + -2/9*((189/4)^(1/2)+6)

x = -(-2/9*((189/4)^(1/2)+6))

x = 2/9*((189/4)^(1/2)+6)

( x-2/9*(6-(189/4)^(1/2)) )

x-2/9*(6-(189/4)^(1/2)) = 0 // + -2/9*(6-(189/4)^(1/2))

x = -(-2/9*(6-(189/4)^(1/2)))

x = 2/9*(6-(189/4)^(1/2))

x in { 2/9*((189/4)^(1/2)+6), 2/9*(6-(189/4)^(1/2)) }

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