SOLUTION: Hi can you explain to me how to simplify the expression l^2m(2-m)/l^3(m-2) . I have the answer in my text book but not sure of the steps required to get there , thanks

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi can you explain to me how to simplify the expression l^2m(2-m)/l^3(m-2) . I have the answer in my text book but not sure of the steps required to get there , thanks       Log On


   

Question 631007: Hi can you explain to me how to simplify the expression
l^2m(2-m)/l^3(m-2) . I have the answer in my text book but not sure of the steps required to get there , thanks

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28l%5E%282m%29%282-m%29%29%2F%28l%5E3%28m-2%29%29
Since one to any power is 1, this simplifies to:
%282-m%29%2F%28m-2%29
The next step is quick if you notice that 2-m and m-2 are negatives of each other. In one the 2 is positive and in the other the 2 is negative. In one the m is negative and in the other the m is positive. So 2-m and m-2 are negatives of each other. (Let that sink in for a while. It can be helpful in other situations, too, to realize that a-b and b-a are negatives of each other.)

And what do you get when you divide negatives? What is -1/1, 20.3/(-20.3), x/(-x), etc.? Answer for all: -1. So (2-m)/(m-2) is:
-1

P.S. In the future, please explain the expression has an "el" in it to avoid confusion. Here's a solution using el's:
%28l%5E%282m%29%282-m%29%29%2F%28l%5E3%28m-2%29%29
We can "un-multiply" the fractions so that you can see better how this works out:
%28l%5E%282m%29%2Fl%5E3%29%2A%28%282-m%29%2F%28m-2%29%29
The (2-m)/(m-2) still works out to be -1. To divide the el's, we use the rule for exponents when dividing expressions with the same base: Subtract the exponents:
l%5E%282m-3%29%2A%28-1%29
or just
-l%5E%282m-3%29