(a) Solve the inequality : (frac{2}{5}(x – 2) – frac{1}{6}(x + 5) leq 0).
(b) Given that P = (frac{x^{2} – y^{2}}{x^{2} + xy}),
(i) express P in its simplest form ; (ii) find the value of P if x = -4 and y = -6.
Explanation
(a) (frac{2}{5}(x – 2) – frac{1}{6}(x + 5) leq 0)
Multiplying through by the LCM of 5 and 6 (i.e 30)
(12(x – 2) – 5(x + 5) leq 0)
(12x – 24 – 5x – 25 leq 0)
(7x – 49 leq 0 implies 7x leq 49)
(x leq 7).
(b) (i) (frac{x^{2} – y^{2}}{x^{2} + xy})
P = (frac{(x – y)(x + y)}{x (x + y)})
P = (frac{x – y}{x})
(ii) When x = -4, y = -6
(P = frac{-4 – (-6)}{-4})
(P = frac{2}{-4})
(P = – frac{1}{2})