Week 11 — Readings & Resources
Your primary reading is Chapter 11 (in this module). Everything below is the optional, go-deeper layer — pick what helps, skip the rest.
How to use this page
This page has 10 items (4 readings and 6 videos). Allow 79–92 minutes for everything. Each group points back to the matching chapter section and class-session segment, so use the full menu when you want more practice, or take the quick path below.
Every video here has captions: turn them on with the CC button in the player. The chapter covers the same ideas in text.
Pick-one quick path (20–23 min total)
- Tutorial 8: Simplifying Rational Expressions — Virtual Math Lab
- Extraneous Solutions of Rational Equations — The Organic Chemistry Tutor
① When may I cancel? Simplifying, multiplying, and dividing
Chapter 11, Section “Simplify by factoring first: cancel factors, never terms” · Session 1, Segment 2, “Simplifying, multiplying, and dividing” · Remember: factor the top and the bottom first, cancel only a factor that multiplies everything, and keep the excluded values.
- Tutorial 8: Simplifying Rational Expressions — Virtual Math Lab — a short tutorial that first finds the values a rational expression must exclude because they make the bottom zero, then factors the top and the bottom and cancels only common factors; use it while working through the Week-11 module overview. (reading, 6–9 min)
- Simplifying Rational Expressions — Mathispower4u — several expressions factored and reduced, with the excluded values found from the original bottom before anything cancels. (video, 8 min) (captions: creator)
- Multiplying and Dividing Rational Expressions — Mathispower4u — products and quotients done the same careful way, including flipping only the divisor before cancelling. (video, 8 min) (captions: creator)
② How do I add them? Building the least common denominator
Chapter 11, Section “Add and subtract over a least common denominator built from factors” · Session 1, Segment 3, “Adding and subtracting” · Remember: factor every bottom, build the LCD from those factors, and let a minus sign reach the whole second top.
- Rational Functions, Equations, and Inequalities — Math Hints — a tutor's guide whose sections on finding the common denominator and on adding and subtracting build the least common denominator from each bottom's factors, rewrite every fraction over it, and warn you to push a minus sign through the whole second top; read those two sections and skip the inequalities. This builds on Week 6's work with factoring polynomials. (reading, 8–12 min)
- Adding and Subtracting Rational Expressions — Patrick J — short worked sums and differences, each rewritten over a shared bottom before the tops are combined. (video, 8 min) (captions: automatic)
- Adding and Subtracting Rational Expressions With Unlike Denominators — The Organic Chemistry Tutor — a long run of examples with different bottoms, good for practice when one example is not enough. (video, 13 min) (captions: automatic)
③ Why throw an answer out? Rational equations and work rates
Chapter 11, Section “Solve a rational equation and reject what fails” · Session 2, Segment 5, “Solving rational equations” · Remember: write the excluded values first, clear the LCD, solve, and reject any candidate that makes a bottom zero.
- Solving Rational Equations — ChiliMath — a run of worked equations that find the least common denominator, clear the fractions, and check each answer for values that make a denominator zero. (reading, 8–12 min)
- Extraneous Solutions of Rational Equations — The Organic Chemistry Tutor — several equations solved by clearing the denominators, with every candidate checked against the original and the extraneous ones rejected. (video, 14 min) (captions: automatic)
- Rate Problem: Two Buckets Filling Tank — Intuitive Math — a short take on two sources filling one tank, where the rates add and the time together comes out shorter than either alone. (video, 3 min) (captions: automatic)
Optional one-stop reference (free online reference)
- Rational Function — Wolfram MathWorld — a mathematics encyclopedia's entry; read the opening definition of a quotient of two polynomials, and skip the later remarks on poles in the complex plane and partial fractions, which go beyond this course. (reading, 3–5 min)
Heads-up (links rot): these point to outside sites that occasionally move or rename pages. If a link ever fails, tell your instructor and use the reference above in the meantime.
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