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what exactly is addition and subtraction of rational expressions?

Can someone define and give me examples.

A "rational expression" is a fraction in which the numerator and denominator are polynomials. For instance,

( x + 2 ) / ( 2x - 3 ) and ( 3x - 3 ) / ( x + 1 )

are rational expressions.

To add or subtract them, you first give them common denominators. For instance, say you desire to add the above expressions:

( x + 2 ) / ( 2x - 3 ) + ( 3x - 3 ) / ( x + 1 )

Give them a common denominator:

( x + 2 ) ( x + 1 ) / ( 2x - 3 ) ( x + 1 ) + ( 3x - 3 ) ( 2x - 3 ) / ( x + 1 ) ( 2x - 3 )

Now add the numerators:

[ ( x + 2 ) ( x + 1 ) + ( 3x - 3 ) ( 2x - 3 ) ] / ( 2x - 3 ) ( x + 1 )

Further simplification is left as an exercise for the reader :)

This entry was posted on Monday, September 14th, 2009 at 8:16 pm and is filed under subtraction. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

One Response to “what exactly is addition and subtraction of rational expressions?”

  1. jgoulden Says:
    September 15th, 2009 at 1:48 am

    A "rational expression" is a fraction in which the numerator and denominator are polynomials. For instance,

    ( x + 2 ) / ( 2x - 3 ) and ( 3x - 3 ) / ( x + 1 )

    are rational expressions.

    To add or subtract them, you first give them common denominators. For instance, say you desire to add the above expressions:

    ( x + 2 ) / ( 2x - 3 ) + ( 3x - 3 ) / ( x + 1 )

    Give them a common denominator:

    ( x + 2 ) ( x + 1 ) / ( 2x - 3 ) ( x + 1 ) + ( 3x - 3 ) ( 2x - 3 ) / ( x + 1 ) ( 2x - 3 )

    Now add the numerators:

    [ ( x + 2 ) ( x + 1 ) + ( 3x - 3 ) ( 2x - 3 ) ] / ( 2x - 3 ) ( x + 1 )

    Further simplification is left as an exercise for the reader :)
    References :

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