SOLUTION: Please help! I need to express the following rational expression in lowest terms: x^3+5x^2 --------- 2x^2+9x-5

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Question 195828: Please help! I need to express the following rational expression in lowest terms:
x^3+5x^2
---------
2x^2+9x-5
Found 3 solutions by solver91311, jim_thompson5910, vleith:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Factor both the numerator and denominator expressions. You will find that there is a common factor that can be eliminated.


John

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The key to these types of problems is factoring and canceling out common terms.


%28x%5E3%2B5x%5E2%29%2F%282x%5E2%2B9x-5%29 Start with the given expression.


%28x%5E2%28x%2B5%29%29%2F%282x%5E2%2B9x-5%29 Factor x%5E3%2B5x%5E2 to get x%5E2%28x%2B5%29.


%28x%5E2%28x%2B5%29%29%2F%28%28x%2B5%29%282x-1%29%29 Factor 2x%5E2%2B9x-5 to get %28x%2B5%29%282x-1%29.


%28x%5E2%2Ahighlight%28%28x%2B5%29%29%29%2F%28highlight%28%28x%2B5%29%29%282x-1%29%29 Highlight the common terms.


%28x%5E2%2Across%28%28x%2B5%29%29%29%2F%28cross%28%28x%2B5%29%29%282x-1%29%29 Cancel out the common terms.


%28x%5E2%29%2F%282x-1%29 Simplify.


So %28x%5E3%2B5x%5E2%29%2F%282x%5E2%2B9x-5%29 simplifies to %28x%5E2%29%2F%282x-1%29.


In other words, %28x%5E3%2B5x%5E2%29%2F%282x%5E2%2B9x-5%29=%28x%5E2%29%2F%282x-1%29 where x%3C%3E-5 or x%3C%3E1%2F2

Answer by vleith(2983) About Me  (Show Source):