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1953 AMC 12 Question 7

AMC12 · 1953 AMC 12

Question 7

The fraction $$
\frac{\sqrt{a^2+x^2}-\dfrac{x^2-a^2}{\sqrt{a^2+x^2}}}{a^2+x^2}
$$ reduces to:
  1. $0$
  2. $\dfrac{2a^2}{a^2+x^2}$
  3. $\dfrac{2x^2}{(a^2+x^2)^{\frac{3}{2}}}$
  4. $\dfrac{2a^2}{(a^2+x^2)^{\frac{3}{2}}}$
  5. $\dfrac{2x^2}{a^2+x^2}$