(a) (i) Simplify: (3x² - 12) / (x² + x - 6)

(ii) Hence, or otherwise, solve: (3x² - 12) / (x² + x - 6) = 6

(b) The sum of two numbers is 15 and the sum of their squares is 137. Find the two numbers.

(c) Solve the inequality: (2x - 1)/3 - (x + 2)/2

Question

(a) (i)  Simplify: (3x² - 12) / (x² + x - 6)

(ii) Hence, or otherwise, solve: (3x² - 12) / (x² + x - 6) = 6

(b) The sum of two numbers is 15 and the sum of their squares is 137. Find the two numbers.

(c) Solve the inequality: (2x - 1)/3 - (x + 2)/2 < 1, and represent the solution on a number line.

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