(20x/x^2-25)/(x^3-4x^2-5x/4x^2)

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Solution for (20x/x^2-25)/(x^3-4x^2-5x/4x^2) equation: 


D( x )

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

x^2 = 0

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

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

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

-1/4*x^3-4*x^2 = 0

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

1/4*x+4 = 0 // - 4

1/4*x = -4 // : 1/4

x = -4/1/4

x = -16

-x^2 = 0

-1*x^2 = 0 // : -1

x^2 = 0

x = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in (-oo:-16) U (-16:0) U (0:+oo)

((20*x)/(x^2)-25)/(x^3-(((5*x)/4)*x^2)-(4*x^2)) = 0

((20*x)/(x^2)-25)/(x^3+(-5/4)*x^3-4*x^2) = 0

(20*x^-1-25)/(-1/4*x^3-4*x^2) = 0

-1/4*x^3-4*x^2 = 0

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

1/4*x+4 = 0 // - 4

1/4*x = -4 // : 1/4

x = -4/1/4

x = -16

-x^2*(x+16) = 0

(20*x^-1-25)/(-x^2*(x+16)) = 0

20*x^-1 = 25 // : 20

x^-1 = 5/4

-1 < 0

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

1 = 5/4*x^1 // : 5/4

4/5 = x^1

x = 4/5

x = 4/5

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