What are the critical points for the inequality x^2 - 4/x^2 - 5x +6 < 0?
a. x = –2 and x = 2
b. x = 2 and x = 3
c. x = –3, x = –2, and x = 2
d. x = –2, x = 2, and x = 3

Critical points are: 2 , -2 and 3.

Step-by-step explanation:

We have been given the expression:

We will factorize the given expression:

Using

Critical point are those values of an expression when it is equal to zero

Hence, the critical points are: 2,-2 and -3.

d. x = –2, x = 2, and x = 3 are critical points.

Step-by-step explanation:

Given : < 0.

To find :What are the critical points for the inequality.

Solution : We have given that

< 0.

Using

< 0.

Now, on factoring denominator

Taking commom

x( x- 3) -2(x -3)

On grouping (x-3)(x -2)

.

We need to find critical point ,

Critical point on which expression is zero

Then x = 2, -2, 3 are critical point.

Therefore, d. x = –2, x = 2, and x = 3 are critical points.

c

step-by-step explanation: