((3x-5)/(x^2-9))1

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Solution for ((3x-5)/(x^2-9))1 equation: 


D( x )

x^2-9 = 0

x^2-9 = 0

x^2-9 = 0

1*x^2 = 9 // : 1

x^2 = 9

x^2 = 9 // ^ 1/2

abs(x) = 3

x = 3 or x = -3

x in (-oo:-3) U (-3:3) U (3:+oo)

(3*x-5)/(x^2-9) < 1 // - 1

(3*x-5)/(x^2-9)-1 < 0

(3*x-5)/(x^2-9)+(-1*(x^2-9))/(x^2-9) < 0

3*x-1*(x^2-9)-5 < 0

3*x-x^2+4 < 0

3*x-x^2+4 = 0

3*x-x^2+4 = 0

DELTA = 3^2-(-1*4*4)

DELTA = 25

DELTA > 0

x = (25^(1/2)-3)/(-1*2) or x = (-25^(1/2)-3)/(-1*2)

x = -1 or x = 4

(x+1)*(x-4) = 0

((x+1)*(x-4))/(x^2-9) < 0

((x+1)*(x-4))/(x^2-9) < 0 // * (x^2-9)^2

(x+1)*(x-4)*(x^2-9) < 0

( x+1 )

x+1 < 0 // - 1

x < -1

( x-4 )

x-4 < 0 // + 4

x < 4

( x^2-9 )

1*x^2 < 9

1*x^2 < 9 // : 1

x^2 < 9/1

x^2 < 9

x^2 < 9 // ^ 1/2

abs(x) < 3

x in (-3:3)

	(-oo:-3)	(-3:-1)	(-1:3)	(3:4)	(4:+oo)
x+1	-	-	+	+	+
x-4	-	-	-	-	+
x^2-9	+	-	-	+	+


x in (-3:-1) U (3:4)

(-3:-1) U (3:4)

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