Example 1

Write the reciprocal of x2 + x + 1/x-1

Reciprocal of is

Reciprocal of

Example 2

Similarly, we express the division by a non-zero rational expression to be the same as multiplication with its reciprocal.

Example 3

Example 4

Express as a rational expression

Example 5

Try these questions

I. Write the reciprocals of

1. 




2. 




3. 

Answers to the questions

I. Solutions

1. To find the reciprocal of

   Comparing with the reciprocal of p(x) /q(x) is q(x)/p(x)

   
   

   Reciprocal of




2. To find the reciprocal of

   Comparing with the reciprocal of p(x) /q(x) is q(x)/p(x))

   Reciprocal of




3. To find the reciprocal of

   Comparing with the reciprocal of p(x) /q(x) is q(x)/p(x)

   
   

   Reciprocal of

II. Simplify

1. 

2. 

3. 

Answers to the questions

II. Solutions

1. To simplify    

   
   

   Comparing with       

   




2. To simplify    

   
   

   Comparing with       

   




3. To simplify    

   
   

   Comparing with