Question

a.   Simplify

Giving your answer in the form  , where a is an integer.

b.    Hence, or otherwise, simplify

Giving your answer in the form , where b and c is are integers and .

Solution

a.
 

We are given;

Since ;

Since ;

b.    

We are given;

We have found in (a) that;

Therefore;

If we need a rational number in the denominator of a fraction, we need to follow procedure of  “denominator rationalization” as given below.

ü If the denominator is of the form  then multiply both numerator and denominator by .

ü If the denominator is of the form  then multiply both numerator and denominator by  .

ü If the denominator is of the form  then multiply both numerator and denominator by  .

Since ;