SOLUTION: z^2-7z+10/z^2+4z-45

Algebra ->  Rational-functions -> SOLUTION: z^2-7z+10/z^2+4z-45      Log On


   

Question 146498: z^2-7z+10/z^2+4z-45
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28z%5E2-7z%2B10%29%2F%28z%5E2%2B4z-45%29 Start with the given expression.


%28%28z-2%29%2A%28z-5%29%29%2F%28z%5E2%2B4z-45%29 Factor z%5E2-7z%2B10 to get %28z-2%29%2A%28z-5%29.


%28%28z-2%29%2A%28z-5%29%29%2F%28%28z%2B9%29%2A%28z-5%29%29 Factor z%5E2%2B4z-45 to get %28z%2B9%29%2A%28z-5%29.


%28%28z-2%29highlight%28z-5%29%29%2F%28%28z%2B9%29highlight%28z-5%29%29 Highlight the common terms.


%28%28z-2%29cross%28z-5%29%29%2F%28%28z%2B9%29cross%28z-5%29%29 Cancel out the common terms.


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


So %28z%5E2-7z%2B10%29%2F%28z%5E2%2B4z-45%29 simplifies to %28z-2%29%2F%28z%2B9%29.


In other words, %28z%5E2-7z%2B10%29%2F%28z%5E2%2B4z-45%29=%28z-2%29%2F%28z%2B9%29 where z%3C%3E-9 or z%3C%3E5