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−25as 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−25is a rational number for all positive integer values of nnn.
281 exam-style questions on CCEA A Level Maths 3.1 Algebra and functions (A-level only), covering 3.1.1 Algebra and functions (A-level only), 3.1.2 Algebra and functions (A-level only), 3.1.3 Algebra and functions (A-level only), 3.1.4 Algebra and functions (A-level only), 3.1.5 Algebra and functions (A-level only), 3.1.6 Algebra and functions (A-level only), 3.1.7 Algebra and functions (A-level only), 3.1.8 Algebra and functions (A-level only), 3.1.9 Algebra and functions (A-level only), and 3.1 Algebra and functions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.