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System Message

[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Guest (Customer)

[00:00:00] Find the domain of the rational function. x-6/x^2-4=

[00:00:08] hello

Kathy W (Tutor)

[00:00:09] Welcome to Tutor.com !
Let's get started.

[00:00:20] Have you worked with these type of problems before?

Guest (Customer)

[00:01:02] no

Kathy W (Tutor)

[00:01:10] alright, not a problem

[00:01:19] so whenever we are looking for the domain

[00:01:32] we are looking for all possible values of x that can work in this equation

Guest (Customer)

[00:01:49] k

Kathy W (Tutor)

[00:02:18] no what we want to focus is what values do not work for this equation

[00:02:46] so we look at the denominator

Guest (Customer)

[00:02:52] k

Kathy W (Tutor)

[00:03:00] when the denominator is 0, what happens?

Guest (Customer)

[00:03:15] I am not sure

Kathy W (Tutor)

[00:04:24] when we have a 0 in the denominator, there is no solution

[00:04:39] for example if we had 3/0

[00:04:50] is there anything we can multiply to 0 to get us 3?

Guest (Customer)

[00:05:11] no

Kathy W (Tutor)

[00:05:17] right!

[00:05:32] so whenever the denominator is = 0, there is no solution

[00:05:38] so with this problem

Guest (Customer)

[00:05:48] k

[00:05:52] i have another one

Kathy W (Tutor)

[00:05:53] let's focus on when the denominator is = 0

[00:06:04] and that tells us what values do not work for this function

[00:06:15] so we can set the denominator equal to 0

[00:06:20] and see what values we get

[00:06:43] can you solve what's in red?

Guest (Customer)

[00:06:56] no

Kathy W (Tutor)

[00:07:34] ok, here we need to find out for what values of x make the equation equal to zero

[00:07:40] have you worked with factoring?

Guest (Customer)

[00:07:48] yes

Kathy W (Tutor)

[00:08:22] almost!

[00:08:34] there you go!

[00:08:44] and now we just set those two factors equal to 0

[00:09:20] because once either one of them is 0

[00:09:26] the whole product is zero

[00:09:29] so now solve for x

[00:09:34] for both factors

[00:09:54] can you do that for us here?

[00:10:38] i'll do the first one and you can do that other one

[00:11:08] do you see what I just did?

[00:11:14] we need to solve for x

[00:11:22] can you try that with the other one?

[00:12:01] so our two values are -2 and 2

[00:12:17] so that means in the original equation

[00:12:34] whenever x is equal to 2 or -2

[00:12:40] we'll get a no solution

Guest (Customer)

[00:12:47] k

Kathy W (Tutor)

[00:12:50] because we will have 0 in the denominator

[00:12:54] which doesn't not work

[00:13:01] so the domain in the case would be

[00:13:19] all real numbers except for when x =2 or x = -2

[00:13:32] depending on how your teacher wants you to write it

[00:13:39] here's one possible way

[00:14:06] meaning x cannot equal those two values

[00:14:13] Does that make sense?

Guest (Customer)

[00:14:45] yes

Kathy W (Tutor)

[00:15:05] Do you have any questions about anything we went over today?

Guest (Customer)

[00:15:32] no

[00:15:33] tks

Kathy W (Tutor)

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