Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Module: Week 11 of 16 · Fall 2026 · in-person, two 75-minute sessions
Objective covered: Objective 7 — Simplify, operate on, and solve rational expressions and equations, identifying extraneous solutions.

This file holds two pieces: (A) the Module 11 Overview page ("Start Here") and (B) the Welcome Announcement that drips out when the module opens. Dates below assume a Tuesday/Thursday session pattern with Week 11 meeting Tue Nov 10 and Thu Nov 12 (Veterans Day — Nov 11, Wednesday — is a campus holiday; note the shifted session), and end-of-week work due Sunday Nov 15, 11:59 p.m. Adjust the day-of-week and times to match your section.

(A) Module 11 Overview — Start Here

Welcome to Week 11: Rational Expressions & Equations

This is your home base for the week. Read it first, then work the checklist below from top to bottom. Everything you need is linked inside the module.

Note: Wednesday, November 11 is Veterans Day — no class. Our two sessions this week are Tuesday Nov 10 and Thursday Nov 12.

This week we move from rational functions (Week 10's end behavior and asymptotes) to the algebra you need to operate on them: simplifying, combining, and solving. The central idea is that a rational expression is just a fraction — and every fraction rule you know still works, as long as you factor first and cancel factors, not terms.

The week's big question

"A fraction is a fraction — so why do so many rational-expression mistakes come from trying to cancel things that aren't factors?"

By Sunday you'll simplify a rational expression by factoring and canceling, add and subtract with a least common denominator, solve a rational equation by clearing the LCD, and flag any extraneous solutions before they cost you points.

By the end of this week, you can…

Use this as a checklist. If you can do all four, you're ready for the quiz.

• [ ] Simplify a rational expression by factoring the numerator and denominator completely and canceling common factors (never terms).
• [ ] Multiply and divide rational expressions by factoring, flipping (for division), and canceling before multiplying.
• [ ] Add and subtract rational expressions by finding the LCD, building equivalent fractions, and combining numerators.
• [ ] Solve a rational equation by multiplying through by the LCD to clear fractions, solving the resulting polynomial, and checking every solution against the excluded values to catch extraneous roots.

What's due this week, and when

Work these in order — each one gets you ready for the next.

Heads-up on the AI tutorial: chatbots love to cancel terms instead of factors — they'll happily tell you (x+3)/x = 3. Catching that error is part of the job this week.

Veterans Day note: Campus is closed Wednesday Nov 11. Our sessions are Tuesday and Thursday as usual. If you're at an observance or service event this week, reach out before deadlines — I'd much rather hear from you early.

Late policy reminder: 10% off per day late. If life happens, reach out before the deadline.

How to succeed this week

• Factor first, always. Before you cancel a single thing, factor numerator and denominator completely. You can only cancel factors (entire expressions that are multiplied together) — never terms (things that are added or subtracted).
• The cardinal sin. Writing (x + 3)/x = 3 is the most common mistake this week. The x is a term in the numerator, not a factor. You can only cancel when the same expression divides every term in the numerator AND sits as a factor in the denominator.
• LCD is your friend. For adding/subtracting and for solving: factor the denominators, build the LCD from all distinct factors (each to its highest power), multiply every term by the LCD, and simplify. If the resulting equation is linear or quadratic, you already know how to finish it.
• Always check for extraneous solutions. After solving, plug your answer back into the original equation. Any value that makes a denominator zero in the original is excluded — if your solution hits one of those, it's extraneous and you write "no solution" (or discard it if there are multiple solutions).
• Use the chatbot as a drafting tool, not an oracle. This week especially, chatbots make term-cancellation errors. The AI-critique moment in the tutorial exists specifically because of this pattern.

The algebra is familiar — it's the same factoring you mastered in Week 6, the same fraction rules you've used since middle school. The new move is doing those things with polynomial numerators and denominators, and checking your answers at the end.

(B) Welcome Announcement — Module 11

Release setting: post on the module's start day (offset = 0 days), i.e., Mon Nov 9, 2026 (or the night before for early readers). If your platform won't preserve the scheduled date on import, post this as a draft labeled "Release: Mon Nov 9."

Subject: Week 11 — the algebra of fractions, done properly 👋

Hi everyone —

Quick reminder first: Veterans Day (Wednesday, Nov 11) is a campus holiday — no class that day. Our two sessions this week are Tuesday and Thursday as usual. If you're attending a ceremony or observance, reach out before the assignment deadlines.

Now to the math. This week we tackle Rational Expressions & Equations — basically, algebra where the quantities are fractions with polynomials on top and bottom. The good news: every rule you already know about numerical fractions applies here. The danger: one very tempting mistake that causes more lost points than almost anything else in College Algebra.

The mistake is this: looking at (x + 3)/x and crossing out the x to get 3. The x in the numerator is a term — something added — not a factor — something multiplied. And you can only cancel factors. This week you'll find that mistake, fix it, and never make it again.

Three things not to miss:
1. Lecture Tutorial 11 — you'll work through simplifying, multiplying, adding, and solving rational expressions with an approved chatbot (Gemini, Claude, or ChatGPT). The tutor ends with an AI-critique moment where you catch the chatbot making the exact cancellation error above. Due Sun Nov 15.
2. Quiz 11 (no AI) and Discussion 11 — "The Illegal Cancellation" also close Sun Nov 15 — initial post by Fri Nov 13.
3. Assignment 11 — "Fractions All the Way Down" — four AI-coached problems, self-scored report; due Sun Nov 15.

One week from now you'll be able to simplify rational expressions, combine them with a common denominator, solve rational equations, and spot an extraneous solution before it bites you. That's real algebraic fluency — and it shows up everywhere in the exponential and logarithmic work coming in Weeks 13–15.

Open the Start Here / Module Overview page first. See you Tuesday.

Prof. Calloway