b298e2…: “Behind the stormy castle”

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Let $M(n) = \frac {n}{n+5} + \frac {2n}{n-3}$

Let $a$ and $b$ be real numbers.

Evaluate

\[ M(a+b) = \answer {\frac {a+b}{a+b+5} + \frac {2(a+b)}{a+b-3}} \]

Evaluate

\[ M(a)+b = \answer {\frac {a}{a+5} + \frac {2a}{a-3} +b} \]

Evaluate

\[ a \, M(n)+b = \answer {a(\frac {n}{n+5} + \frac {2n}{n-3})+b} \]

2025-05-21 17:05:39