Simplify then solve or apply

First simplify a combination of algebraic fractions into a single fraction, then use the result to solve an equation or answer a further question.

3 questions · Moderate -0.1

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Edexcel C3 Q29
6 marks Moderate -0.3
  1. Express as a fraction in its simplest form $$\frac{2}{x-3} + \frac{13}{x^2 + 4x - 21}.$$ [3]
  2. Hence solve $$\frac{2}{x-3} + \frac{13}{x^2 + 4x - 21} = 1.$$ [3]
Edexcel C3 Q3
6 marks Moderate -0.3
  1. Express as a fraction in its simplest form $$\frac{2}{x - 3} + \frac{13}{x^2 + 4x - 21}.$$ [3]
  2. Hence solve $$\frac{2}{x - 3} + \frac{13}{x^2 + 4x - 21} = 1.$$ [3]
Edexcel C3 Q4
9 marks Standard +0.3
  1. Express $$\frac{x-10}{(x-3)(x+4)} - \frac{x-8}{(x-3)(2x-1)}$$ as a single fraction in its simplest form. [5]
  2. Hence, show that the equation $$\frac{x-10}{(x-3)(x+4)} - \frac{x-8}{(x-3)(2x-1)} = 1$$ has no real roots. [4]