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02.23.2019: One Lesson of Math - Unit Review - Rational Expressions and Equations


Today's soundtrack is Hillsong: United We Stand, an upbeat "praise and worship" album that all the members of the church band that I used to drum in were compelled to purchase when the worship leader decided that we were going to learn all of the songs on the album and play them identically to the album version.


When we asked if the church could provide us copies so that not all ten of us would have to buy a copy at ~$15 a pop, we were told "No, but it's a really good album, so it's worth it to buy!" Okay then. Never mind the fact that the worship leader was the only one being paid to be part of the worship team. So not only were we expected to come early, stay for both services, leave late, come in for mid-week evening practices, and practice at home, we were expected to buy CDs so that we could have the "privilege of serving."


One of my other fond memories of being part of that worship team was how the worship leader would record footage of our "performances," then play back the footage and critique our "image" (the bassist wasn't moving enough, the guitarist wasn't close enough to the front of the stage, the singer should have been clapping more there)! The whole thing was just one big act, an over-produced stage show.


/rant

 

I've reached the end of Unit 7, the final unit in my precalculus 11 course. I'm doing my unit review assignment today, which covers the following:


  1. Equivalent Rational Expressions

  2. Part 1

  3. Part 2

  4. Part 3

  5. Multiplying and Dividing Rational Expressions

  6. Part 1

  7. Part 2

  8. Part 3

  9. Part 4

  10. Adding and Subtracting Rational Expressions With Monomial Denominators

  11. Part 1

  12. Part 2

  13. Part 3

  14. Adding and Subtracting Rational Expressions With Binomial and Trinomial Denominators

  15. Part 1

  16. Part 2

  17. Solving Rational Equations

  18. Part 1 (includes the Rational Root Theorem and Synthetic Division)

  19. Part 2

  20. Part 3


Here's a little cheat-sheet:

  • Equivalent rational expressions

  • Multiply both numerator and denominator by the same values

  • Multiplying and Dividing Rational Expressions

  • Factor, cancel out the common factors, then multiply

  • Multiply by reciprocal to divide

  • Adding and Subtracting Rational Expressions

  • Multiply each expression's numerator and denominator of by the denominator of the other expression, then combine and simplify

  • Solving Rational Equations

  • Multiply all denominators together to get a common denominator. Multiply each numerator by all that common denominator. Cancel out identical terms from numerators and denominators. Solve algebraically.

 

A side note - here's why I'm glad that I started using Forest: It stops me from distracting myself with random Google searches!

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