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UKMT Intermediate Mathematical Challenge, 2023

Algebra Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

What is the positive difference between the numerator and the denominator when the expression shown is written as a single fraction in its simplest form? $\dfrac{n}{n+1-\dfrac{n+2}{n+3}}$

(A) $2n+2$ (B) $n+2$ (C) $n$ (D) $2$ (E) $1$

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