Equations with algebraic denominators

Equations with algebraic denominators

Secondary 2
TGM Original Questions

Solve each of the following equations, checking denominator restrictions.

  1. \(\frac{3a}{a-2}=\frac{8-4a}{a^2-4}\)
  2. \(\frac{2y}{y-1}=1+\frac{y}{y+2}\)
  3. \(\frac4m+\frac5{m+2}=1\)
  4. \(\frac{x}{x+3}=\frac3{x-2}+1\)
  5. \(\frac4{3x}+1=\frac1{x^2}\)
  6. \(\frac1{m+2}+\frac3{m^2-4}=1\)

Solution:

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Answer:(a) \(a=\frac23,-4\); (b) \(y=-\frac12\); (c) \(m=8,-1\); (d) \(x=-\frac12\); (e) \(x=\frac{-2\pm\sqrt{13}}3\); (f) \(m=\frac{1\pm\sqrt{21}}2\).

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