x-45/x-4

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Solution for x-45/x-4 equation: 


D( x )

x = 0

x = 0

x = 0

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

x-(45/x) < -4 // + 4

x-(45/x)+4 < 0

x-45*x^-1+4 < 0

x-45*x^-1+4 = 0

1*x^1-45*x^-1+4*x^0 = 0

(1*x^2+4*x^1-45*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^2+4*x^1-45*x^0) = 0

x^1

x^2+4*x-45 = 0

x^2+4*x-45 = 0

DELTA = 4^2-(-45*1*4)

DELTA = 196

DELTA > 0

x = (196^(1/2)-4)/(1*2) or x = (-196^(1/2)-4)/(1*2)

x = 5 or x = -9

x in { -9, 5} 

(x+9)*(x-5) < 0

	(-oo:-9)	(-9:5)	(5:+oo)
x+9	-	+	+
x-5	-	-	+


x in (-9:0) U (0:5)

(-9:0) U (0:5)

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