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AMO · 2027 · Grades 8-9 · Self-study SET 23 Question 9

AMO

Question 9

Constants $M,N$ satisfy the identity
$$\frac{52x+73}{14x^2+83x+33}=\frac{M}{7x+3}+\frac{N}{2x+11}.$$
Find $MN-M-N$. The identity holds for all real $x$ for which the denominators are nonzero.
  1. 19
  2. 13
  3. 16
  4. -22
  5. 7