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Math Help - Simplifying algebraic fractions

  1. #1
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    Simplifying algebraic fractions

    Hello! I have a problem in my textbook that I am working through. It involves simplifying this:

    \frac{8(a^2 - b^2)}{3(a+2)} \div \frac{4(a-b)}{27(a+1)}

    I get as far as this...

    \frac{18(a^2 - b^2)(a+1)}{(a+2)(a-b)}

    Now, according to the book, I can simplify that to:

    \frac{18(a+b)(a+1)}{(a+2)}

    I can see that it works, but I'm not sure why. I don't know what rule they used to do that. Can you please explain why that worked?
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  2. #2
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    Re: Simplifying algebraic fractions

    Quote Originally Posted by joebard View Post
    Hello! I have a problem in my textbook that I am working through. It involves simplifying this:

    \frac{8(a^2 - b^2)}{3(a+2)} \div \frac{4(a-b)}{27(a+1)}

    I get as far as this...

    \frac{18(a^2 - b^2)(a+1)}{(a+2)(a-b)}

    Now, according to the book, I can simplify that to:

    \frac{18(a+b)(a+1)}{(a+2)}

    I can see that it works, but I'm not sure why. I don't know what rule they used to do that. Can you please explain why that worked?
    You are supposed to know that

    a^2-b^2 = (a+b)(a-b)

    so you can cancel the factor (a - b)
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