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Division of Rational Expressions

http://www.redcomet.org/Ma45a/jj247.gif
 

Example 1

Write the reciprocal of x2 + x + 1/x-1
 
Reciprocal of http://www.redcomet.org/Ma45a/jj247.gif is http://www.redcomet.org/Ma45a/jj246.gif
 

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.

http://www.redcomet.org/Ma45a/p97.gif

3.

http://www.redcomet.org/Ma45a/p98.gif

Answers to these questions

I. Solutions

1.

To find the reciprocal of

http://www.redcomet.org/Ma45a/p96.gif

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


Reciprocal of

http://www.redcomet.org/Ma45a/p107.gif

 

2.

To find the reciprocal of

http://www.redcomet.org/Ma45a/p97.gif


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


Reciprocal of

http://www.redcomet.org/Ma45a/p108.gif

 

3.

To find the reciprocal of

http://www.redcomet.org/Ma45a/p98.gif

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

The reciprocal of

http://www.redcomet.org/Ma45a/p109.gif

II. Simplify

1.

http://www.redcomet.org/Ma45a/p99.gif

2.

http://www.redcomet.org/Ma45a/p100.gif

3.

http://www.redcomet.org/Ma45a/p102.gif

Answers to these questions

II. Solutions

1.

To simplify

http://www.redcomet.org/Ma45a/p99.gif

   

Comparing with

http://www.redcomet.org/Ma45a/p110.gif

http://www.redcomet.org/Ma45a/p112.gif

 

2.

To simplify

http://www.redcomet.org/Ma45a/p100.gif

   

Comparing with

http://www.redcomet.org/Ma45a/p110.gif

http://www.redcomet.org/Ma45a/p113.gif

 

3.

To simplify

http://www.redcomet.org/Ma45a/p102.gif

   

Comparing with

http://www.redcomet.org/Ma45a/p110.gif

http://www.redcomet.org/Ma45a/p114.gif

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