SOLUTION: Perform the indicated operation. Give the answer in lowest terms. {(z^2 + 4z + 4)/(z^2 + 9z + 14)}/{(z^2 + 2z)/(z^2 + 4z - 21)} I beleive thats how it would be displayed, its

Algebra ->  Equations -> SOLUTION: Perform the indicated operation. Give the answer in lowest terms. {(z^2 + 4z + 4)/(z^2 + 9z + 14)}/{(z^2 + 2z)/(z^2 + 4z - 21)} I beleive thats how it would be displayed, its      Log On


   

Question 201042: Perform the indicated operation. Give the answer in lowest terms.
{(z^2 + 4z + 4)/(z^2 + 9z + 14)}/{(z^2 + 2z)/(z^2 + 4z - 21)}
I beleive thats how it would be displayed, its two fractions divided by each other.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given expression.


Multiply the first fraction %28z%5E2%2B4z%2B4%29%2F%28z%5E2%2B9z%2B14%29 by the reciprocal of the second fraction %28z%5E2%2B2z%29%2F%28z%5E2%2B4z-21%29.


Factor z%5E2%2B4z%2B4 to get %28z%2B2%29%28z%2B2%29.


Factor z%5E2%2B9z%2B14 to get %28z%2B7%29%2A%28z%2B2%29.


Factor z%5E2%2B4z-21 to get %28z%2B7%29%2A%28z-3%29.


Factor z%5E2%2B2z to get z%2A%28z%2B2%29.


Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


%28z-3%29%2Fz Simplify.



So simplifies to %28z-3%29%2Fz.


In other words,