SOLUTION: simplify this expression: (x-5)^3/|x-5| I have the answer:(x-5)*|x-5|, but do not know how to get there

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Question 203523: simplify this expression: (x-5)^3/|x-5|
I have the answer:(x-5)*|x-5|, but do not know how to get there
Answer by jsmallt9(3296) About Me  (Show Source):
You can put this solution on YOUR website!
One of the earliest lessons you learn about absolute value is that the absolute value of a positive number is that number. This is also true of the absolute value of 0. And finally the absolute value of a negative number is that number without its minus sign. Another way to express this is: The absolute value of a negative number is the negative of that negative number. Expressing these ideas in mathematical notation:
if a+%3E=+0, then abs%28a%29+=+a
if a+%3C++0, then abs%28a%29+=+-a
We will use these to simplify: %28x-5%29%5E3%2Fabs%28x-5%29

Case: x-5+%3E=+0
If x-5+%3E=+0, then abs%28x-5%29+=+x-5 so your expression becomes:
%28x-5%29%5E3%2F%28x-5%29
This simplifies to
%28x-5%29%5E2+=+%28x-5%29%28x-5%29
Substituting abs%28x-5%29 in for %28x-5%29 (Remember they are equal if x-5+%3E=+0 which is true in this case):
%28x-5%29%2Aabs%28x-5%29

Case: x+-+5+%3C+0
If x-5+%3C+0, then abs%28x-5%29+=+-%28x-5%29 so your expression becomes:
%28x-5%29%5E3%2F%28-%28x-5%29%29
This simplifies to
-%28x-5%29%5E2+=+-%28x-5%29%28x-5%29
Substituting abs%28x-5%29 in for -%28x-5%29 (Remember they are equal if x-5+%3C+0 which is true in this case):
abs%28x-5%29%2A%28x-5%29+=+%28x-5%29abs%28x-5%29

In either case we end up with %28x-5%29abs%28x-5%29.