(x-5)^2/x^2-9=0

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Solution for (x-5)^2/x^2-9=0 equation: 


D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

((x-5)^2)/(x^2)-9 >= 0

((x-5)^2)/(x^2)+(-9*x^2)/(x^2) >= 0

(x-5)^2-9*x^2 >= 0

25-8*x^2-10*x >= 0

25-8*x^2-10*x = 0

25-8*x^2-10*x = 0

DELTA = (-10)^2-(-8*4*25)

DELTA = 900

DELTA > 0

x = (900^(1/2)+10)/(-8*2) or x = (10-900^(1/2))/(-8*2)

x = -5/2 or x = 5/4

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

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

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

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

( x+5/2 )

x+5/2 >= 0 // - 5/2

x >= -5/2

( x-5/4 )

x-5/4 >= 0 // + 5/4

x >= 5/4

( x^2 )

1*x^2 >= 0

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

x^2 >= 0/1

x^2 >= 0

x in (-oo:+oo)

	(-oo:-5/2)	(-5/2:5/4)	(5/4:+oo)
x+5/2	-	+	+
x-5/4	-	-	+
x^2	+	+	+


x in (-oo:-5/2> U <5/4:+oo)

(-oo:-5/2> U <5/4:+oo)

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