SOLUTION: simplify x^2a /z^3 - a^2 Divided by x/z^2 - 3/z^3

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Question 64849This question is from textbook An Incremental Development
: simplify
x^2a /z^3 - a^2
Divided by
x/z^2 - 3/z^3 This question is from textbook An Incremental Development

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E2a%2Fz%5E3+-+a%5E2%29%2F%28x%2Fz%5E2+-+3%2Fz%5E3%29
Put the a² over 11 so that everything on top 
and bottom will be a fraction.  I used 11 instead
of just 1 because it "stacks up" better using the forum's
notation system.  You can just use 1 where I have 11.
%28x%5E2a%2Fz%5E3+-+a%5E2%2F1%5E1%29%2F%28x%2Fz%5E2+-+3%2Fz%5E3%29
Look at all the denominators on the top and the bottom.
Their LCD is z³. so multiply by z%5E3%2Fz%5E3, written as+%28%28z%5E3%2F1%5E1%29%29%2F%28%28z%5E3%2F1%5E1%29%29


+%28%28z%5E3%2F1%5E1%29%29%2F%28%28z%5E3%2F1%5E1%29%29·%28%28x%5E2a%2Fz%5E3+-+a%5E2%2F1%5E1%29%29%2F%28%28x%2Fz%5E2+-+3%2Fz%5E3%29%29
Now distribute:
     
In the upper left term you can cancel the z³'s, 
     leaving x²a.
The upper right term becomes just -z³a².
In the lower left term, subtract the exponents 
     of the z's and get simply zx.
In the lower right term you can cancel the z³'s,
     leaving -3.

So you end up with:
%28x%5E2a+-+z%5E3a%5E2%29%2F%28zx-3%29
Now if you like you can factor out "a" on top:
a%28x%5E2+-+z%5E3a%29%2F%28zx-3%29
but that step isn't necessary.

Edwin