((5/x)-(1/4))/((25/x^2)-(1/16))

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Solution for ((5/x)-(1/4))/((25/x^2)-(1/16)) equation: 


D( x )

x = 0

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

x^2 = 0

x = 0

x = 0

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

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

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

25*x^-2 = 1/16 // : 25

x^-2 = 1/400

-2 < 0

1/(x^2) = 1/400 // * x^2

1 = 1/400*x^2 // : 1/400

400 = x^2

x^2 = 400 // ^ 1/2

abs(x) = 20

x = 20 or x = -20

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in (-oo:-20) U (-20:0) U (0:20) U (20:+oo)

(5/x-(1/4))/(25/(x^2)-(1/16)) = 0

(5/x-1/4)/(25/(x^2)-1/16) = 0

(5*x^-1-1/4)/(25*x^-2-1/16) = 0

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

x^-1 = 1/20

-1 < 0

1/(x^1) = 1/20 // * x^1

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

20 = x^1

x = 20

x in { 20} 

x belongs to the empty set

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