What you posted meant:
But I doubt that is the real problem. I suspect it is supposed to be:
If this is correct, then it should be posted as:
((x^2-1)/(x^2-9)) * ((x^2-8x-9)/(x^2-3x+2))
Each numerator and denominator has parentheses around it and the two fractions are factors so they get parentheses around them, too.
Now to the problem. Way back in the "good old days" when fractions just had numbers in them, you learned that you could either dive right in with the multiplication or simplify the fractions before multiplying. As part of this simplification, you were allowed to "cross-cancel" (cancel a factor from one fraction's numerator with the other fraction's denominator and vice versa). (Note: Multiplying fractions is the only time you are allowed to cross-cancel!!). In summary, when multiplying fractions your choices are:
Multiply then reduce; or
Reduce then multiply then maybe reduce again.
The second way seems like more work (3 steps instead of 2) but it is actually the best way to go most of the time. For example:
If we multiply first then we get:
Then we would have to try to reduce this. Finding factors of 756 and 588 that are equal will not be simple.
On the other hand we could reduce first:
Cancel:
leaving:
which is much easier to multiply than : (which cannot be reduced so we are finished.)
Note: If you are careful and reduce the fractions fully before multiplying then after multiplying you will not need to reduce again. But it's a good idea to check for reducing at the end anyway.
By reducing first we reduced with smaller numbers (which is easier than with large numbers) and the multiplication itself was easier. Perhaps you do not yet feel that there is really that much advantage to reducing first. But as the fractions get more complicated, like:
the greater the advantage there is in reducing first. The last thing I would want to do with your problem is to start by actually multiply out the fractions and then trying to reduce the mess you end up with!
So we will start by factoring each numerator and denominator to see if there are any factors we can cancel:
And we can see that there are some factors we can cancel:
leaving:
Although we did not simplify very much, this expression will still be easier to multiply than what we started with. Since the 1st denominator and the 2nd numerator were not reduced we already know what they multiply to:
Finishing the multiplication...
And since we know we fully reduced at the start we know that this fraction will not reduce. So we are finished.
(