Simplifying algebraic fractions

**joebard** · July 10th 2011, 09:42 AM

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?

**earboth** · July 10th 2011, 09:48 AM

Originally Posted by joebard

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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