The curve C has equation y = 5(x – 1)(x + 2)/(x – 2)(x + 3).

i. Express y in the form P + Q/x – 2 + R/x + 3.

ii. Show that dy/dx = 0 for exactly one value of x and find the corresponding value of y.

iii. Write down the equations of all the asymptotes of C.

iv. Find the set of values of k for which the line y = k does not interest C.