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Math Help - Help reducing a fraction to lowest terms...

  1. #1
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    Help reducing a fraction to lowest terms...

    Hi guys,

    I'm new here, been reading some questions for a while just out of curiosity, learned a thing or two along the way!

    I'm doing my homework and I'm stuck on this problem. I need to reduce the following fraction to lowest terms. What do you guys think would be the best way to go about it? I'm getting a bit confused as to where I should start...



    Thanks a lot guys! I appreciate the help!

    Egoyan
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  2. #2
    MHF Contributor

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    Re: Help reducing a fraction to lowest terms...

    Of course, you want to factor those and see if anything in numerator and denominator cancel.

    Looking at these, I think you want to use a couple of "well known" products: x^3- y^3= (x- y)(x^2+ xy+ y^2) and x^2- y^2= (x- y)(x+ y).

    For example, (a+ 6)^3- (b- 6)^3= (a+6- (b- 6))((a+6)^2+ (a+ b)(b- 6)+ (b+ 6)^2) where I have taken x= a+ 6 and y= b- 6.

    And, (a+ 6)^4- (b- 6)^4= ((a+ 6)^2)^2- ((b- 6)^2)^2= ((a+ 6)^2- (b- 6)^2)((a+ 6)^2+ (b+ 6)^2) with x= (a+ 6)^2 and y= (b- 6)^2. Then, further (a+ 6)^2- (b- 6)^2= (a+ 6- (b- 6))(a+ 6+ (b- 6)).
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  3. #3
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    Re: Help reducing a fraction to lowest terms...

    Ah! I see. Thanks a lot! I'm going to try this way.
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