SOLUTION: z^2-8z+15/z^2+2z-35 this is a fraction

Algebra ->  Expressions-with-variables -> SOLUTION: z^2-8z+15/z^2+2z-35 this is a fraction       Log On


   

Question 150626: z^2-8z+15/z^2+2z-35 this is a fraction
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28z%5E2-8z%2B15%29%2F%28z%5E2%2B2z-35%29 Start with the given expression.


%28%28z-3%29%2A%28z-5%29%29%2F%28z%5E2%2B2z-35%29 Factor z%5E2-8z%2B15 to get %28z-3%29%2A%28z-5%29.


%28%28z-3%29%2A%28z-5%29%29%2F%28%28z%2B7%29%2A%28z-5%29%29 Factor z%5E2%2B2z-35 to get %28z%2B7%29%2A%28z-5%29.


%28%28z-3%29highlight%28z-5%29%29%2F%28%28z%2B7%29highlight%28z-5%29%29 Highlight the common terms.


%28%28z-3%29cross%28z-5%29%29%2F%28%28z%2B7%29cross%28z-5%29%29 Cancel out the common terms.


%28z-3%29%2F%28z%2B7%29 Simplify.


So %28z%5E2-8z%2B15%29%2F%28z%5E2%2B2z-35%29 simplifies to %28z-3%29%2F%28z%2B7%29.


In other words, %28z%5E2-8z%2B15%29%2F%28z%5E2%2B2z-35%29=%28z-3%29%2F%28z%2B7%29 where z%3C%3E-7 or z%3C%3E5