Solve Rational Inequalities

Question

x^2-x-2/x^2+5x+6<0

I cant figure this out. Please help

First try to factor whenever you can to determine critical solutions:

(x - 2)(x + 1) / (x + 3)(x + 2) < 0

Critical solutions:
x = 2
x = -1
x = -3
x = -2

Test 5 intervals using a number line:

<==== -3 == -2 == -1 === 0 ====== 2 ===>

x < -3 ...let's choose -4. If we choose -4 for x, the result will be positive and not less than 0.
-3 < x < -2 ...let's choose -5/2. If we choose -5/2 for x, the result will be negative and less than 0.
-2 < x < -1 ...let's choose -3/2. If we choose -3/2 for x, the result will be negative and less than 0.
-1 < x < 2 ...let's choose 0. If we choose 0 for x, the result will be negative and less than 0.
x > 2 ...let's choose 3. If we choose 3 for x, the result will be positive and not less than 0.

Three of the tests work. If you are familiar with interval notation, the solution set can be written this way:
(-3,-2)U(-2,-1)U(-1,2) -->U = union of sets.

Answer 1

Which of the following will have a negative result? (1 point)
A–8 – ( –10 )
B12 – 14
C7 – ( –3 )

Answer 2

C7 – ( –3 )

Answer 3

Select the word that best completes the statement.
The difference of two positive integers is _____ negative.
(1 point)
always
sometimes
never

Answer 4

Sometimes.

Answer 5

-24 - 5 =

Answer 6

-29.

Answer 7

-4 -(- 16 ) =

Answer 8

12.

Answer 9

_4 - ( - 16 ) =

Answer 10

20.

Answer 11

-4 - ( - 16 ) =

a 30
b -30
c 2
d -2

Answer 12

Answer: c) 2.

-4 - ( - 16 ) = -4 + 16 = 12.

Answer 13

Which of the following is equivalent to (–2) – 5?

Answer 14

(–2) – 5 is equivalent to -7.

Answer 15

Which of the following is equivalent to (–2) – 5?

A -2 + (-5)
B -2 + 5
C 2 + ( -5 )

Answer 16

A -2 + (-5) is equivalent to (–2) – 5.