SOLUTION: Simplify: (t^2 + t - 6) / (t^2 - 7t + 10) A question at De La Salle High School, New Orleans Mu Alpha Theta tournament.

Algebra ->  Expressions-with-variables -> SOLUTION: Simplify: (t^2 + t - 6) / (t^2 - 7t + 10) A question at De La Salle High School, New Orleans Mu Alpha Theta tournament.      Log On


   

Question 236472: Simplify: (t^2 + t - 6) / (t^2 - 7t + 10)
A question at De La Salle High School, New Orleans Mu Alpha Theta tournament.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28t%5E2%2Bt-6%29%2F%28t%5E2-7t%2B10%29 Start with the given expression.


%28%28t%2B3%29%28t-2%29%29%2F%28t%5E2-7t%2B10%29 Factor t%5E2%2Bt-6 to get %28t%2B3%29%28t-2%29.


%28%28t%2B3%29%28t-2%29%29%2F%28%28t-2%29%2A%28t-5%29%29 Factor t%5E2-7t%2B10 to get %28t-2%29%28t-5%29.


%28%28t%2B3%29highlight%28%28t-2%29%29%29%2F%28highlight%28%28t-2%29%29%28t-5%29%29 Highlight the common terms.


%28%28t%2B3%29cross%28%28t-2%29%29%29%2F%28cross%28%28t-2%29%29%28t-5%29%29 Cancel out the common terms.


%28t%2B3%29%2F%28t-5%29 Simplify.


So %28t%5E2%2Bt-6%29%2F%28t%5E2-7t%2B10%29 simplifies to %28t%2B3%29%2F%28t-5%29.


In other words, %28t%5E2%2Bt-6%29%2F%28t%5E2-7t%2B10%29=%28t%2B3%29%2F%28t-5%29