Week 11 — Readings & Resources · Rational Expressions & Equations

Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Objective covered: Objective 7 — Simplify, operate on, and solve rational expressions and equations, identifying extraneous solutions.

How to use this page

Everything here is a link to an external resource — open it in your browser, the same way you'd open a YouTube link. Nothing needs to be downloaded.

This week's load is deliberately focused: 2 readings + 2–3 videos, grouped by the four ideas from the lecture. Read or watch one item per group and you're ready for the quiz; do all of them and you'll be very comfortable. Total time is roughly 35–55 minutes if you do everything, far less if you pick one per group.

Reading order that matches the lecture: ① simplifying rational expressions → ② multiplying & dividing → ③ adding & subtracting (LCD) → ④ solving rational equations & checking for extraneous solutions.

A habit to keep: the AI tutorial ends with a critique moment where you catch the chatbot making a term-cancellation error. Keep that posture as you read — factor first, check the algebra.

Heads-up (links rot): these point to outside sites that occasionally move or rename pages. If a link ever fails, tell Prof. Calloway and use Paul's Online Math Notes at tutorial.math.lamar.edu in the meantime.

① & ② Simplifying, Multiplying, and Dividing Rational Expressions

Maps to Lecture Segments 2–3. The rule that never changes: factor first, cancel factors (never terms), and state the excluded values.

Reading — "Rational Expressions" (OpenStax, College Algebra 2e, §1.6)
🔗 https://openstax.org/books/college-algebra-2e/pages/1-6-rational-expressions
Why it's assigned: covers simplifying, multiplying, dividing, and adding/subtracting rational expressions in one clean section, with worked examples that follow the same factor-then-cancel method used in class. Read the "Simplifying Rational Expressions," "Multiplying Rational Expressions," and "Dividing Rational Expressions" parts for this group.
⏱ ~12 min

Reading — "Rational Expressions" (Paul's Online Math Notes — Algebra)
🔗 https://tutorial.math.lamar.edu/classes/alg/RationalExpressions.aspx
Why it's assigned: tight, step-by-step page that nails the term-vs-factor distinction and walks through several simplification, multiplication, and division examples with commentary on what goes wrong. Excellent second pass if a step didn't click in class.
⏱ ~10 min

③ Adding and Subtracting with an LCD

Maps to Lecture Segment 4. Factor the denominators, build the LCD, convert every fraction, and combine numerators — watching the sign on subtraction.

Reading — "Rational Expressions" (OpenStax, College Algebra 2e, §1.6, continued)
🔗 https://openstax.org/books/college-algebra-2e/pages/1-6-rational-expressions
Why it's assigned: the "Adding and Subtracting Rational Expressions" part of the same §1.6 section shows the LCD method, with sign-error callouts on subtraction.
⏱ ~8 min (same link as above, continue reading)

Video — "Adding and Subtracting Rational Expressions" (Professor Leonard — Intermediate Algebra Lecture 7.4)
🔗 https://www.youtube.com/watch?v=kv3xoX4v2Yo
Why it earns the click: an unhurried, full-board walkthrough of the LCD method for polynomial denominators — Professor Leonard shows every step and calls out the sign-distribution trap explicitly.
⏱ longer lecture (skim to the LCD setup and the first two examples)

④ Solving Rational Equations & Extraneous Solutions

Maps to Lecture Segments 5–6. Clear by LCD, solve the resulting equation, and — always — check every solution against the excluded values before you write it down.

Reading — "Other Types of Equations" (OpenStax, College Algebra 2e, §2.6 — rational-equations portion)
🔗 https://openstax.org/books/college-algebra-2e/pages/2-6-other-types-of-equations
Why it's assigned: the "Solving Rational Equations Resulting in a Quadratic" and surrounding examples in §2.6 show exactly how to clear denominators and why extraneous solutions appear. Scroll to the rational-equations portion (after the radical equations section).
⏱ ~8 min

Video — "Solving Rational Equations" (Professor Leonard — Intermediate Algebra Lecture 7.5)
🔗 https://www.youtube.com/watch?v=iHOl4Ia2r-g
Why it earns the click: detailed board-work showing the LCD-clearing method, with multiple examples that produce extraneous solutions — Professor Leonard pauses to explain why they arise and how to catch them.
⏱ longer lecture (watch the first three worked examples, ~15–20 min)

Optional one-stop references (free online)

If you'd like one reference to return to all term, Paul's Online Math Notes — Algebra keeps full, free notes online, and Professor Leonard's Intermediate Algebra playlist has full-length lectures for every rational-expression topic in this course.

🔗 Paul's Algebra notes: https://tutorial.math.lamar.edu/classes/alg/alg.aspx
🔗 Professor Leonard — Intermediate Algebra playlist: https://www.youtube.com/channel/UCoHhuummRZaIVX7bD4t2czg
Why they're here: reputable, currently-available references you can return to in later weeks — entirely optional this week.

Pick-one quick path (≈15 min total)

In a hurry? Do exactly these and you'll be ready for the quiz:
1. Read OpenStax §1.6 — Rational Expressions (simplifying, multiplying/dividing, and adding/subtracting).
2. Read Paul's Notes — Rational Expressions (reinforces the factor-first rule).
3. Watch the first 15 min of Professor Leonard Lecture 7.5 (solving rational equations and catching extraneous solutions).