The sum of two quantities is y. One of the quantities varies directly as x² and the other inversely as x. If y = 32 when x = 2 and y = 86 when x = 4, find: (a) an equation for y in terms of x. (b) the value of y when x = 3.

Given $\sin x = \frac{8}{17}$.
Using the identity $\sin^2 x + \cos^2 x = 1$:

$$\cos^2 x = 1 - \sin^2 x$$ $$\cos x = \sqrt{1 - \left(\frac{8}{17}\right)^2}$$ $$\cos x = \sqrt{1 - \frac{64}{289}}$$ $$\cos x = \sqrt{\frac{289 - 64}{289}}$$ $$\cos x = \sqrt{\frac{225}{289}}$$ $$\cos x = \frac{15}{17}$$

Given $\sin y = \frac{5}{13}$.
Using the identity $\sin^2 y + \cos^2 y = 1$:

$$\cos^2 y = 1 - \sin^2 y$$ $$\cos y = \sqrt{1 - \left(\frac{5}{13}\right)^2}$$ $$\cos y = \sqrt{1 - \frac{25}{169}}$$ $$\cos y = \sqrt{\frac{169 - 25}{169}}$$ $$\cos y = \sqrt{\frac{144}{169}}$$ $$\cos y = \frac{12}{13}$$

$$\frac{\sin x - \cos y}{\cos x + \sin y} = \frac{\frac{8}{17} - \frac{12}{13}}{\frac{15}{17} + \frac{5}{13}}$$

To simplify, find a common denominator for the numerator and the denominator. The least common multiple of 17 and 13 is $17 \times 13 = 221$.

$$\frac{\frac{8 \times 13}{17 \times 13} - \frac{12 \times 17}{13 \times 17}}{\frac{15 \times 13}{17 \times 13} + \frac{5 \times 17}{13 \times 17}}$$ $$\frac{\frac{104}{221} - \frac{204}{221}}{\frac{195}{221} + \frac{85}{221}}$$ $$\frac{\frac{104 - 204}{221}}{\frac{195 + 85}{221}}$$ $$\frac{\frac{-100}{221}}{\frac{280}{221}}$$ $$\frac{-100}{221} \times \frac{221}{280}$$ $$\frac{-100}{280}$$ $$-\frac{10}{28}$$ $$-\frac{5}{14}$$

The final answer is $\boxed{-\frac{5}{14}}$.