SOLUTION: can you express the following rational expression in lowest term z^3 + 4z^2/z^2 + 8z + 16

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Question 173384: can you express the following rational expression in lowest term
z^3 + 4z^2/z^2 + 8z + 16
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28z%5E3%2B4z%5E2%29%2F%28z%5E2%2B8z%2B16%29 Start with the given expression.


%28z%5E2%28z%2B4%29%29%2F%28z%5E2%2B8z%2B16%29 Factor z%5E3%2B4z%5E2 to get z%5E2%28z%2B4%29.


%28z%5E2%28z%2B4%29%29%2F%28%28z%2B4%29%28z%2B4%29%29 Factor z%5E2%2B8z%2B16 to get %28z%2B4%29%28z%2B4%29.


%28z%5E2%2Ahighlight%28%28z%2B4%29%29%29%2F%28highlight%28%28z%2B4%29%29%28z%2B4%29%29 Highlight the common terms.


%28z%5E2%2Across%28%28z%2B4%29%29%29%2F%28cross%28%28z%2B4%29%29%28z%2B4%29%29 Cancel out the common terms.


z%5E2%2F%28z%2B4%29 Simplify.


So %28z%5E3%2B4z%5E2%29%2F%28z%5E2%2B8z%2B16%29 simplifies to z%5E2%2F%28z%2B4%29.