Week 11 — Rational Expressions & Equations
Welcome to your Week 11 Start Here page.
Why this matters
Rational expressions are how a pharmacy technician works out a dose per kilogram and how a contractor figures how long two crews take together. Cancel only true factors, and check every answer.
In plain language
This week you work with rational expressions (fractions with a polynomial on the top and on the bottom). You will simplify them by cancelling only the pieces that multiply everything, and you will multiply, divide, add, and subtract them. Then you will solve equations that contain them and throw out extraneous solutions (answers that come from correct steps but still fail the original equation). The payoff is real: these equations tell you how long two workers take together and how a shared cost changes as a group grows.
- Already covered: Week 6 taught factoring; Week 7 solved quadratic equations; Week 10 told asymptotes from holes.
- This week: simplifying and combining rational expressions, then solving rational equations and work-rate problems.
- How they connect: every cancel is a Week 6 factoring move, and every cleared equation is one you already know how to solve.
- Where we're going next: Week 12, Radicals, Rational Exponents & Radical Equations, checks every candidate the same way.
Focus
When algebra sits on the bottom of a fraction, how do you simplify, combine, and solve without keeping an answer that fails?
By the end of this module, you should be able to:
- [ ] find excluded values and cancel factors, never terms
- [ ] multiply, divide, add, and subtract rational expressions
- [ ] solve a rational equation and reject an extraneous solution
- [ ] add rates, not times, in a work problem
To-do
Plan your week
- Read Chapter 11 (about 45 minutes), then the lecture and slides.
- Work the lecture tutorial (60–90 minutes) and the practice set (about 20 minutes).
- Do the Model/Build Studio (about 90 minutes), the discussion, and the assignment.
- Take the quiz.
This week's checkpoint: simplify (x² − 9) ⁄ (x + 3) with its restriction and check it at one input.
You've got this
Take it in order, and ask your instructor early if a step snags.
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