Express 5+53−5\displaystyle \frac{5 + \sqrt{5}}{3 - \sqrt{5}}3−55+5 in the form a+b5a + b\sqrt{5}a+b5, where a a\,a and b b\,b are integers.
233 exam-style questions on Edexcel A Level Maths Algebraic Expressions, covering 1.1 Index Laws, 1.2 Expanding Brackets, 1.3 Factorising, 1.4 Negative and Fractional Indices, and 1.5 Surds. Each one has a worked solution and a mark scheme showing where the marks go.