Assume that the sum of a rational number and an irrational number is rational:
ab+i=cd \frac{a}{b} + i = \frac{c}{d} ba+i=dcwhere a,b,c,d a, b, c, d\,a,b,c,d are integers. Show that
i=cb−adbd i = \frac{cb - ad}{bd} i=bdcb−adHence prove by contradiction that the sum of a rational number and an irrational number is irrational
368 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division. Each one has a worked solution and a mark scheme showing where the marks go.