Question

Please help me solve for

Answer 1

9. ( x + 5 ) / ( x + 2 ) < 0 <=> ( x + 5 < 0 and x + 2 > 0 ) or ( x + 5 > 0 or x + 2 < 0 ) <=> ( x < -5 and x > - 2 ) or ( x > -5 and x < -2 ) <=> ( x∈Ф ) or ( - 5 < x < - 2 ) <=> - 5 < x < - 2.

The answer is the fourth choice.

Answer 2

`(x)/(x+1) < (x)/(x-1) \\ (x)/(x+1) - (x)/(x-1) <0 \\ x( (1)/(x+1) - (1)/(x+1))<0 \\ (2x)/(x^2-1) <0`
Consider the function and define the domain of the function

`y=(2x)/(x^2-1)`

`x^2-1 \\eq 0 \\ x^2 \\eq 1 \\ x \\eq \pm 1`
Function is zero

`(2x)/(x^2-1)=0 \\ 2x=0 \\ x=0`

Answer:
`(-1;0)\cup(1;+\infty)`