SOLUTION: How do you simplify an rational expression like: 6-y/y^2-2y-24, whats the answer?

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Question 152265: How do you simplify an rational expression like: 6-y/y^2-2y-24, whats the answer?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Remember, the key to simplifying rational expressions or fractions is to factor


%286-y%29%2F%28y%5E2-2y-24%29 Start with the given expression.


%28-%28y-6%29%29%2F%28y%5E2-2y-24%29 Factor 6-y to get -%28y-6%29.


%28-%28y-6%29%29%2F%28%28y%2B4%29%2A%28y-6%29%29 Factor y%5E2-2y-24 to get %28y%2B4%29%2A%28y-6%29.


%28-highlight%28%28y-6%29%29%29%2F%28%28y%2B4%29highlight%28%28y-6%29%29%29 Highlight the common terms.


%28-cross%28%28y-6%29%29%29%2F%28%28y%2B4%29cross%28%28y-6%29%29%29 Cancel out the common terms.


-%281%29%2F%28y%2B4%29 Simplify.


So %286-y%29%2F%28y%5E2-2y-24%29 simplifies to -%281%29%2F%28y%2B4%29.


In other words, %286-y%29%2F%28y%5E2-2y-24%29=-%281%29%2F%28y%2B4%29 where y%3C%3E-4 or y%3C%3E6