SOLUTION: u^3/w ÷ uv^3/w^2

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Question 151296: u^3/w ÷ uv^3/w^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28u%5E3%29%2F%28w%29%29%2F%28%28uv%5E3%29%2F%28w%5E2%29%29 Start with the given expression.



%28%28u%5E3%29%2F%28w%29%29%28%28w%5E2%29%2F%28uv%5E3%29%29 Multiply the first fraction by the reciprocal of the second fraction.



%28%28u%5E3%29%28w%5E2%29%29%2F%28%28w%29%28uv%5E3%29%29 Combine the fractions.


%28u%5E3w%5E2%29%2F%28uv%5E3w%29 Multiply


%28u%2Au%2Au%2Aw%2Aw%29%2F%28u%2Av%2Av%2Av%2Aw%29 Expand. Remember, u%5E3w%5E2=u%2Au%2Au%2Aw%2Aw and uv%5E3w=u%2Av%2Av%2Av%2Aw


Highlight the common terms.


Cancel out the common terms.


%28u%2Au%2Aw%29%2F%28v%2Av%2Av%29 Simplify.


%28u%5E2%2Aw%29%2F%28v%5E3%29 Regroup.


So %28%28u%5E3%29%2F%28w%29%29%2F%28%28uv%5E3%29%2F%28w%5E2%29%29 simplifies to %28u%5E2%2Aw%29%2F%28v%5E3%29.


In other words, %28%28u%5E3%29%2F%28w%29%29%2F%28%28uv%5E3%29%2F%28w%5E2%29%29=%28u%5E2%2Aw%29%2F%28v%5E3%29 where u%3C%3E0, v%3C%3E0, or w%3C%3E0