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.
16 exam-style questions on Edexcel A Level Maths 1.2 Algebraic Fractions. Each one has a worked solution and a mark scheme showing where the marks go.