Simplifying rational expressions (for review!)

This sequence of videos uses many different variables and works out the problems in detail (yea!), though perhaps doesn’t include quite enough plus/minus signs (so keep an eye out).

  1. \rhd Introduction to simplification of rational expressions (15:22)  These videos include a proper treatment of excluded values. (Hooray!)      –[Example 1] \frac{3}{6}
    –[Example 2] \frac{8}{24}
    –[Example 3] \frac{9x+3}{12x+4}
    –[Example 4] \frac{x^2-9}{5x+15}
    –[Example 5] \frac{x^2 + 6x + 5}{x^2 - x -2}
    –[Example 6] \frac{3x^2 +3x - 18}{2x^2 + 5x - 3} (factoring by grouping)
  2.  \rhd Simplify rational expressions with common monomial factors (0:55) \frac{28b^6}{7b} = 4b^5
  3. \star Simplify the rational expression with common monomial factors \frac{3n^4+6n^3}{6n^4 + 9n^3}
  4. \rhd Simplifying rational expressions with common binomial factors. (4:11)   Given a rectangle with width w = z^2-9 and length $latex  l = z^2 +6a –
    27$, find the ratio of the width to the length of the rectangle.
  5.  \rhd Simpifying Rational Expressions: opposite (sign) common binomial factors x-a and a-x.  (3:53)  \frac{x^2 - 36}{6-x} = -(x+6)
  6.   \star Simplifying rational expressions with common binomial factors  \frac{2z^2 - 288}{z^2 - 9z - 36} What is the domain of the simplified expression?
  7. \rhd Simplifying Rational Expressions: Advanced Factorization (Grouping) (6:41)  \frac{2x^2 + 13x + 20}{2x^2 + 17x + 30} = \frac{(x+4)(2x+5)}{(x+6)(2x+5)}
    What is the domain of the resulting expression?
  8.  \star Simplify the rational expression Simplify the rational expression \frac{5k^2 -26k +5}{25k^3 - k}