Algebraic fractions: adding and dividing

Starter: calculate some additions of ordinary numerical fractions, and then of algebraic fractions.

The rule is the same: first change the fractions so as to get a common denominator (bottom term).

Do division of algebraic terms, so as to get an answer which minimises the number of different appearances of x and separates out the x3, x2, x, etc. terms:

a) by long division

b) by the remainder theorem.