Given that nnn is a positive integer, express
52+3n−53n−2\frac{5}{2+3\sqrt{n}} - \frac{5}{3\sqrt{n}-2}2+3n5−3n−25
as a single fraction not involving surds.
Hence, deduce that
52+3n−53n−2\frac{5}{2+3\sqrt{n}} - \frac{5}{3\sqrt{n}-2}2+3n5−3n−25
is a rational number for all positive integer values of nnn.
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.