SOLUTION: divide and simplify z^2-49/z /z+7/z+9 this is a fraction divided by a fraction

Algebra ->  Expressions-with-variables -> SOLUTION: divide and simplify z^2-49/z /z+7/z+9 this is a fraction divided by a fraction       Log On


   

Question 150627: divide and simplify
z^2-49/z /z+7/z+9 this is a fraction divided by a fraction
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28%28z%5E2-49%29%2F%28z%29%29%2F%28%28z%2B7%29%2F%28z%2B9%29%29 Start with the given expression.


%28%28z%5E2-49%29%2F%28z%29%29%28%28z%2B9%29%2F%28z%2B7%29%29 Multiply the first fraction %28z%5E2-49%29%2F%28z%29 by the reciprocal of the second fraction %28z%2B7%29%2F%28z%2B9%29.


%28%28%28z-7%29%28z%2B7%29%29%2F%28z%29%29%28%28z%2B9%29%2F%28z%2B7%29%29 Factor z%5E2-49 to get %28z-7%29%28z%2B7%29.


%28%28z-7%29%28z%2B7%29%28z%2B9%29%29%2F%28z%28z%2B7%29%29 Combine the fractions.


%28%28z-7%29highlight%28%28z%2B7%29%29%28z%2B9%29%29%2F%28z%2Ahighlight%28%28z%2B7%29%29%29 Highlight the common terms.


%28%28z-7%29cross%28%28z%2B7%29%29%28z%2B9%29%29%2F%28z%2Across%28%28z%2B7%29%29%29 Cancel out the common terms.


%28%28z-7%29%28z%2B9%29%29%2F%28z%29 Simplify.


So %28%28z%5E2-49%29%2F%28z%29%29%2F%28%28z%2B7%29%2F%28z%2B9%29%29 simplifies to %28%28z-7%29%28z%2B9%29%29%2F%28z%29.


In other words, where z%3C%3E0, z%3C%3E-7, or z%3C%3E-9