Three-term rational expressions

Three-term rational expressions

Secondary 2
TGM Original Questions

Express each of the following as a single fraction in its simplest form.

  1. \(\frac{3x^2+13x-10}{x^2+5x}+\frac12\)
  2. \(\frac{y-3}{4-3y-y^2}+\frac{y}{y^2+5y+4}\)
  3. \(\frac1{3x-2}+\frac2{4-9x^2}\)
  4. \(\frac{n+2}{1-9n^2}-\frac{n-4}{6n+2}\)
  5. \(\frac5{p-3}-\frac8{6-2p}+\frac4{3(p+3)}\)
  6. \(\frac3{2+5x}+\frac4{4-25x^2}-\frac1{5x-2}\)

Solution:

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Answer:(a) \(\frac{7x-4}{2x}\); (b) \(\frac{y+3}{(y+4)(y^2-1)}\); (c) \(\frac{3x}{(3x-2)(3x+2)}\); (d) \(\frac{(3n-8)(n-1)}{2(1-3n)(1+3n)}\); (e) \(\frac{31p+69}{3(p-3)(p+3)}\); (f) \(\frac{2(5x-6)}{(5x-2)(5x+2)}\).

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