1. ## Simplifying algebraic fractions

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

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

I get as far as this...

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

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

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

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?

2. ## Re: Simplifying algebraic fractions

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

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

I get as far as this...

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

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

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

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

$\displaystyle a^2-b^2 = (a+b)(a-b)$

so you can cancel the factor (a - b)