The difference in signal attenuation, A(k)A(k)A(k), between two experimental microwave waveguides depends on a positive integer parameter kkk according to the formula:
A(k)=83+7k−87k−3 A(k) = \frac{8}{3+7\sqrt{k}} - \frac{8}{7\sqrt{k}-3} A(k)=3+7k8−7k−38Express A(k)A(k)A(k) as a single fraction that does not involve surds.
Hence, deduce that the attenuation difference A(k)A(k)A(k) is a rational number for all positive integer values of kkk.
Practise Edexcel A Level Maths Algebraic Methods with exam-style questions for A Level Maths. 226 questions covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division, 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.
