Solving rational equations

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Examples
Lessons
  1. Solve the following rational equations:
    1. 3−3x=1+1x3-\frac{3}{x}=1+\frac{1}{x}
    2. 2x+15x=132x+\frac{15}{x}=13
  2. Solving Rational Equations by cross multiplying
    State the non-permissible values for the variable x, then solve algebraically.
    1. 8x+4=3x−1 \frac{8}{x+4}=\frac{3}{x-1}
    2. 2x−26x−1=3x+49x+5 \frac{2x-2}{6x-1}=\frac{3x+4}{9x+5}
  3. Solve
    2x−9+20x+9=80x2−81 \frac{2}{x-9}+\frac{20}{x+9}=\frac{80}{x^2-81}
    1. Solve the following equations algebraically:
      1. 2x+2+3x−2=1\frac{2}{x+2}+\frac{3}{x-2}=1
      2. 2t−3t−1−3t+1t+2=−1\frac{2t-3}{t-1}-\frac{3t+1}{t+2}=-1
    2. Solving Rational Equations by factoring
      State the non-permissible values for the variables, then solve algebraically.
      1. x2−5x+4(x−1)=−4 \frac{x^2-5x+4}{(x-1)}=-4
      2. x−1x2−1=12x−3\frac{x-1}{x^2-1}=\frac{1}{2x-3}
    Topic Notes
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    In this lesson, we will learn how to state the non-permissible value(s) of rational equations and how to solve them algebraically.
    Always find the non-permissible values before solving the rational equations as some answers might have to be rejected.