Expert: Steve Holleran - 8/27/2008

Question
a.(ab^-2c^-3)/(a^-2b^-3c^2)
b. (x^2+5x+4)/(x+1)

Answer
Hi George,

Okay, on the first one, the factors with the negative exponents should be moved to the other part of the fraction, and the exponents made positive:

   a b^-2 c^-3
------------------
   a^-2 b^-3 c^2

Move the b^-2 on top to the bottom and make it b^2
Move the c^-3 on top to the bottom and make it c^3
Move the a^-2 on bottom to the top and make it a^2
Move the b^-3 on bottom to the top and make it b^3

So it should look like this:

 a * a^2 * b^3
-----------------
 b^2 * c^3 * c^2

which becomes

  a^3 b^3          and simplified =  a^3 b
-----------                         -------
  b^2 c^5                              c^5



On the second one, you can do this several ways, but the easiest is to factor the numerator:

   x^2 + 5x + 4       (x + 4)(x + 1)
  -------------  =    --------------   =  x + 4.



Steve
       x + 1               x + 1