Question

How could I solve the rational inequality 5/(x+2)>5/x+2/(3x)?

Answer 1

The answer is x<-17

Answer 2

\[\frac{5}{x+2}>\frac{5}{x}+\frac{2}{3x}\]

Answer 3

Shouldn't it also be -2<x<0?

Answer 4

multiply through by [x(x+2)]^2

Answer 5

5x^2 (x+2) > 5x(x+2)^2 +(2/3) x(x+2)^2

Answer 6

Wouldn't that be 3x(x+2)?

Answer 7

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

Answer 8

x(x+2) [ (2/3)(x+2) +5(x+2) -5x] <0

Answer 9

x(x+2)( (2/3)x +(34/3) ) <0

Answer 10

take the (1/3) factor out \[\frac{1}{3}x (x+2)(2x+34) <0 \]

Answer 11

take the (1/3) factor out \[\frac{1}{3}x (x+2)(2x+34) <0 \]

Answer 12

rest is easy.

Answer 13

-2<x<0 and x<-17

Answer 14

yeah I thought so too.

Answer 15

I think I should had searched for the values of x that yield undefined since the beginning when the equation was equaled to zero.

Answer 16

By the way, I appreciate the time you took, no one else responded I truly appreciate it.