SOLUTION: multiply and simplify this: m squared - 9/9m times 7m/(m+3) The answer I got is 7m(m-3)/9m I don't think this is simplified enough. Need steps. I am a homeschool mom and

Algebra ->  Radicals -> SOLUTION: multiply and simplify this: m squared - 9/9m times 7m/(m+3) The answer I got is 7m(m-3)/9m I don't think this is simplified enough. Need steps. I am a homeschool mom and      Log On


   

Question 399998: multiply and simplify this:
m squared - 9/9m times 7m/(m+3) The answer I got is 7m(m-3)/9m
I don't think this is simplified enough. Need steps. I am a homeschool mom and I don't have the answer to this problem to explain to my Algebra II child. Also don't know how to make exponents on the computer!
Angie
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28m%5E2-9%29%2F9m%29%287m%2F%28m%2B3%29%29
When multiplying fractions it is not only OK but a good idea to cancel factors that are common to the numerators and denominators before you multiply. One is even allowed to cancel factors from one fraction across to the other fraction.

So the best place to start is to factor each numerator and denominator. We can factor the first numerator as a difference of squares, a%5E2-b%5E2+=+%28a%2Bb%29%28a-b%29. And we can factor a 1 out of the second denominator:
%28%28%28m%2B3%29%28m-3%29%29%2F%289%2Am%29%29%28%287%2Am%29%2F%281%28m%2B3%29%29%29
Now we can cancel the factors that are common to both the numerators and the denominators:

leaving:
%28%28m-3%29%2F9%29%287%2F1%29
These are much easier to multiply than the original two fractions. Multiplying we get:
%28%28m-3%297%29%2F%289%2A1%29
Except for the m's that I canceled but you did not, this is what you had. This simplifies to:
%287m-21%29%2F9