Question

How do you simplify `( t^2-49)/(t^2+4t-21) * (t^2+8t+15)/(t^2-2t-35)`?

Answer 1

You first factorise, and then see what you can cancel.
Use 'special products' if needed.

Explanation:

`=((t+7)(t-7))/((t+7)(t-3))*((t+3)(t+5))/((t-7)(t+5))`

Now cancel:

`=(cancel((t+7))cancel((t-7)))/(cancel((t+7))(t-3))*((t+3)cancel((t+5)))/(cancel((t-7))cancel((t+5)))`

`=(t+3)/(t-3)`