Day: March 5, 2024

Announcements

Our first midterm exam will be tomorrow (Wed March 6). Please work on the open WebWork sets, especially the exercises listed below; you can also review the exercises exercises listed below from the earlier WebWork sets. The best preparation for the exam is to write out solutions to the homework exercises.

You can also review your class notes and the Class Recaps here on OpenLab, since we did most of these WebWork examples in class. You can review the quiz solutions, which are available on OpenLab Files. You can also review relevant examples from the textbook–the links to the relevant sections of the textbook are listed below.

Here are the WebWork exercises to complete and/or review in preparation for the exam:

• Rational Expressions-Multiplying and Dividing: #2-6 (due tonight – March 5; Sec 1.3.2)
• Rational Expressions-Adding and Subtracting Part 1: #1-6 (due tonight – March 5 – Sec 1.3.3)
• Rational Expressions-Adding and Subtracting Part 2: #1-2 (due Monday March 11 – Sec 1.3.3)
• Polynomials-Factor Trinomials: #1-4 (due Monday March 11 – Sec 1.2.7)

Since the exercises on rational expressions require most of the previous techniques we covered (in particular factoring and simplifying polynomials), you should focus on doing the exercises above. See also the Class Recap below, since we did more examples involving rational expressions, including some of the WebWork exercises listed above.

For review of the previous material, you can review the following exercises from the closed WebWork sets:

• Polynomials-Evaluate Add Subtract Polynomials: #5, 6 (Sec 1.2.2)
• Polynomials-Multiply Polynomials: #1, 4 (Sec 1.2.3)
• Polynomials-Powers of Monomials and Binomials: #3-5 (Sec 1.2.4)
• Polynomials-DividePolynomials: #3 (Sec 1.2.5)
• Polynomials-GCF and Factor by Grouping: #2, 3 (Sec 1.2.6)
• Polynomials-Factor Trinomials AC Method: #5-7 (Sec 1.2.7)
• Rational Expressions-Simplifying: #1-2 (Sec 1.3.2)

Topics

We started with another example of simplifying a rational expression–once again, the main strategy is to factor the polynomials in the numerator and denominator and then cancel common factors.

For this example, we also “evaluated” the given expression at a given numerical value, using the function notation–we evaluated the given rational expression at the values x=1 and x=2 (both in unsimplified and simplified form, verifying that we get the same result):

We went through an exercise from the “RationalExpressions-Adding and Subtracting Part 1” WebWork–in these exercises the given rational expressions have the same denominator, so you just need to add or subtract the numerators (and then simplify):

Another example from “Rational Expressions-Adding and Subtracting Part 1” :

We then did a couple examplex from “Rational Expressions-Adding and Subtracting Part 2”–in these exercises, the given rational expressions have different denominators, so you need to identify the LCD (least common denominator) and then “scale up” each term (by multiplying by “an appropriate form of 1”) so that it has the LCD. This is the same technique you learned for addition/subtraction of rational numbers, i.e., fractions: