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−7A(k) = \frac{12}{7 + 4\sqrt{k}} - \frac{12}{4\sqrt{k} - 7}A(k)=7+4k12−4k−712
Express 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.
Practise Edexcel A Level Maths 1.2 Algebraic Fractions with exam-style questions for A Level Maths. 16 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.