Problem 1

Reduce the following expression to its simplest form:

Solution

1. Working on the first term. Noting that

   and
   
   Hence, the first term becomes

2. Now the second term. Write

   Multiplying by the extra factor gives

   
   Next, simplify
   
   Expand to obtain

   and
   

   Combining gives

Thus the second term becomes

c) Combine the terms. The expression becomes

Expand

Subtracting the second group results in

d) Since , it follows that

Answer: