Solving Rational Equations

The videos on this page are about Solving Rational Equations, also called Fractional Equations.

  1.  \rhd Equations with one rational expression (3:11)  \frac{14x+4}{-3x-2} = 8.
    Solution: x = -\frac{-10}{19}
  2.  \star Solve for r r: \frac{4r-6}{r-7} = \frac{1}{2}
  3. \rhd Solving equations with one rational expression (advanced)   Solve: x^2 - \frac{x^2 - 4}{x-2} = 4 with x \neq 2.
    This produces the equation x^2 - x - 6 = 0, so x = 3 or x = -2.¬† Then he correctly verifies — doesn’t assume the conclusion! (Says: f(-2) = 4 after defining f(x) to be the given rational expression.)
  4. \star Solving equations with one rational expression  Solve \frac{-3k - 38}{k^2 - 16} = -1
  5. \rhd Equations with two rational expressions (4:16)  Solve and find excluded values (p \neq 1, -3). \frac{4}{p-1} = \frac{5}{p+3}  Solution: p = 17, verifies solution.
  6.  \rhd Equations with two rational expressions (by finding the least common multiple) (4:07)  \frac{5}{2x} - \frac{4}{3x} = \frac{7}{18} (note that x \neq 0.  Solution: x = 3
  7.   \rhd Rational equations with extraneous solutions (3:02) Solve: \frac{x^2}{x+2} = \frac{4}{x+2}.  The values x = -2 and x = 2 satisfy the resulting equation, but x = -2 is extraneous.
  8.  \star Equations with two rational expressions  \frac{k+5}{k^2 -5k +6} = \frac{k-9}{k-2}