x-5/x-4

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Solution for x-5/x-4 equation: 


D( x )

x = 0

x = 0

x = 0

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

x-(5/x) < -4 // + 4

x-(5/x)+4 < 0

x-5*x^-1+4 < 0

x-5*x^-1+4 = 0

1*x^1-5*x^-1+4*x^0 = 0

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

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

x^1

x^2+4*x-5 = 0

x^2+4*x-5 = 0

DELTA = 4^2-(-5*1*4)

DELTA = 36

DELTA > 0

x = (36^(1/2)-4)/(1*2) or x = (-36^(1/2)-4)/(1*2)

x = 1 or x = -5

x in { -5, 1} 

(x+5)*(x-1) < 0

	(-oo:-5)	(-5:1)	(1:+oo)
x+5	-	+	+
x-1	-	-	+


x in (-5:0) U (0:1)

(-5:0) U (0:1)

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