In this discussion, you are assigned two rational expressions to work on.

Remember to factor all polynomials completely. Read the following instructions

in order and view the example (available for download in your

online classroom) to complete this discussion. Please find the two rational

expressions assigned to you in the table below. First Rational Expression: 1 – x2 xSecond Rational Expression: 2b – 2 2b2 – 8 Explain in your own words what the meaning of domain is. Also, explain why a

denominator cannot be zero.

Find the domain for each of your two rational expressions.

Write the domain of each rational expression in set notation (as

demonstrated in the example).

Do both of your rational expressions have excluded values in their domains?

If yes, explain why they are to be excluded from the domains. If no, explain why

no exclusions are necessary.

Incorporate the following five math vocabulary words into your discussion.

Use bold font to emphasize the words in your writing. Do not

write definitions for the words; use them appropriately in sentences describing

your math work.

Domain

Excluded value

Set

Factor

Real numbers

Your initial post should be at least 250 words in length. Support your claims

with examples from required material(s) and/or other scholarly resources, and

properly cite any references.**SEE ATTACHED EXAMPLE TO KNOW HOW TO FORMAT THE ANSWER*****ALSO, I MAY HAVE QUESTIONS AFTER I CONFIRM PAYMENT, I WOULD LIKE TO HAVE SOMEONE WHO WILL BE WILLING TO ANSWER ME, AND HELP ME UNDERSTAND THE ANSWER BETTER, EVEN THOUGH HE/SHE HAS BEEN PAID***mat222.w1.discussionexample.pdfINSTRUCTOR GUIDANCE EXAMPLE: Week One Discussion

Domains of Rational Expressions

Students, you are perfectly welcome to format your math work just as I have done in

these examples. However, the written parts of the assignment MUST be done about

your own thoughts and in your own words. You are NOT to simply copy this wording

into your posts!

Here are my given rational expressions oh which to base my work.

25×2 – 4

5 – 9w

67

9w2 – 4

The domain of a rational expression is the set of all numbers which are allowed to

substitute for the variable in the expression. It is possible that some numbers will not be

allowed depending on what the denominator has in it.

In our Real Number System division by zero cannot be done. There is no number (or

any other object) which can be the answer to division by zero so we must simply call the

attempt “undefined.” A denominator cannot be zero because in a rational number or

expression the denominator divides the numerator.

In my first expression, the denominator is a constant term, meaning there is no variable

present. Since it is impossible for 67 to equal zero, there are no excluded values for the

domain. We can say the domain (D) is the set of all Real Numbers, written in set

notation that would look like this:

D = {x| x ∈ ℜ} or even more simply as D = ℜ.

For my second expression, I need to set the denominator equal to zero to find my

excluded values for w.

9w2 – 4 = 0

(3w – 2)(3w + 2) = 0

3w – 2 = 0 or 3w + 2 = 0

3w = 2

or 3w = -2

w = 2/3 or w = -2/3

I notice this is a difference of squares which I can factor.

Set each factor equal to zero.

Add or subtract 2 from both sides.

Divide both sides by 3.

These are the excluded values for my second expression.

The domain (D) for my second expression is the set of all Reals excluding ±2/3. In set

notation, this can be written as D = {w| w ∈ ℜ, w ≠ ±2/3}

Now, both of my expressions do not have excluded values. In one expression, I have no

excluded values because there is no variable in the denominator and a non-zero number

will never just become zero. In the other expression, there are two excluded numbers

because both, if inserted in place of the variable, would cause the denominator to become

zero and thus the whole expression would become undefined.

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