(a) Define the terms “proper rational function” and “improper rational function”.
(b) Let
f(x)=x3−4x2x4−x3+5x+7.
State, with reason, whether f(x) is a proper or an improper rational function.
(c) Before expressing f(x) as a sum of simpler fractions, one algebraic operation must first be carried out. State this operation and explain briefly why it is necessary in the present case.
b. (b) Let f(x)=x3−4x2x4−x3+5x+7. State, with reason, whether f(x) is a proper or an improper rational function.