A researcher is measuring the difference in signal attenuation, AAA, at two distinct observation points. For a positive integer parameter k≥1k \ge 1k≥1, the attenuation is modelled by
A(k)=127+4k−124k−7 A(k) = \frac{12}{7 + 4\sqrt{k}} - \frac{12}{4\sqrt{k} - 7} A(k)=7+4k12−4k−712Express A(k)A(k)A(k) as a single fraction that does not involve surds.
Hence, deduce that A(k)A(k)A(k) is a rational number for all positive integer values of kkk.
