2007 H2 Mathematics

Paper 1 Question 1

(a)

Show that

$\frac{2 x^{2} - x - 19}{x^{2} + 3 x + 2} - 1 = \frac{x^{2} - 4 x - 21}{x^{2} + 3 x + 2} .$

[1]

(b)

Hence, without using a calculator, solve the inequality

$\frac{2 x^{2} - x - 19}{x^{2} + 3 x + 2} > 1 .$

[4]