(7/(x-9))(9/(7x-4))

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Solution for (7/(x-9))(9/(7x-4)) equation: 


D( x )

7*x-4 = 0

x-9 = 0

7*x-4 = 0

7*x-4 = 0

7*x-4 = 0 // + 4

7*x = 4 // : 7

x = 4/7

x-9 = 0

x-9 = 0

x-9 = 0 // + 9

x = 9

x in (-oo:4/7) U (4/7:9) U (9:+oo)

7/(x-9) < 9/(7*x-4) // - 9/(7*x-4)

7/(x-9)-(9/(7*x-4)) < 0

7/(x-9)-9*(7*x-4)^-1 < 0

7/(x-9)-9/(7*x-4) < 0

(7*(7*x-4))/((x-9)*(7*x-4))+(-9*(x-9))/((x-9)*(7*x-4)) < 0

7*(7*x-4)-9*(x-9) < 0

40*x+53 < 0

(40*x+53)/((x-9)*(7*x-4)) < 0

(40*x+53)/((x-9)*(7*x-4)) < 0 // * ((x-9)*(7*x-4))^2

(40*x+53)*(x-9)*(7*x-4) < 0

( 40*x+53 )

40*x+53 < 0 // - 53

40*x < -53 // : 40

x < -53/40

( 7*x-4 )

7*x-4 < 0 // + 4

7*x < 4 // : 7

x < 4/7

( x-9 )

x-9 < 0 // + 9

x < 9

	(-oo:-53/40)	(-53/40:4/7)	(4/7:9)	(9:+oo)
40*x+53	-	+	+	+
7*x-4	-	-	+	+
x-9	-	-	-	+


x in (-oo:-53/40) U (4/7:9)

(-oo:-53/40) U (4/7:9)

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