Division of Rational Expressions


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



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

Answers to the questions

II. Solutions

  1. To simplify    


    Comparing with       


  2. To simplify    


    Comparing with       


  3. To simplify    


    Comparing with