MathNet 2019-part-03 — 184 problems (EN–VI) Question 55

Let $a$ be a real number. Suppose the function $f(x) = \frac{a}{x-1} + \frac{1}{x-2} + \frac{1}{x-6}$ defined in the interval $3 \lt x \lt 5$ attains its maximum at $x = 4$. Find the value of $a$.