Question

a.   Simplify

giving your answer in the form  , where  is an integer.

 

b.   Simplify 

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

Solution

a.
 

We are given;

Since ;

Since ;

b.
 

As demonstrated in (a) we can write the numerator as;

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  .

We have algebraic formula;