SOLUTION: (2x^3+2x)/(x^2-2x)*(x-1)/(4x^2+4)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: (2x^3+2x)/(x^2-2x)*(x-1)/(4x^2+4)      Log On


   

Question 614963: (2x^3+2x)/(x^2-2x)*(x-1)/(4x^2+4)
Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
%28%282x%5E3%2B2x%29%2F%28x%5E2-2x%29%29%2A%28%28x-1%29%2F%284x%5E2%2B4%29%29
Back in the "good old days", when fractions were just made of numbers, you learned:
  • Fractions are reduced by canceling factors that are common to the numerator and the denominator.
  • When multiplying fractions...
    • It is not only OK but it is a very good idea to cancel before you multiply
    • "Cross-canceling" is OK. Cross-canceling is when you cancel a factor of a numerator (or denominator) of one fraction with the same factor in the denominator (or numerator) of another fraction. (You'll see this shortly.)
The same is true with these fractions! In fact, it is even more important then ever to cancel before you actually multiply!!

So we'll start by canceling factors. And to cancel factors we need to know what the factors are. So we factor the numerators and denominators:

Now that we can see the factors, we can see that there are some factors to cancel, including cross-canceling the 2 and the x%5E2%2B1 factors:

leaving
%281%2F%28x-2%29%29%28%28x-1%29%2F2%29
This, you must agree, is a lot easier to multiply than what we started with. Multiplying we get:
%28x-1%29%2F%282x-4%29