SOLUTION: X2 + 3x - 10 X2 -x-2 ___________ divided by __________ x+3 X+1

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Question 150925: X2 + 3x - 10 X2 -x-2
____________ divided by __________
x+3 X+1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28x%5E2%2B3x-10%29%2F%28x%2B3%29%29%2F%28%28x%5E2-x-2%29%2F%28x%2B1%29%29 Start with the given expression.


%28%28x%5E2%2B3x-10%29%2F%28x%2B3%29%29%28%28x%2B1%29%2F%28x%5E2-x-2%29%29 Multiply the first fraction %28x%5E2%2B3x-10%29%2F%28x%2B3%29 by the reciprocal of the second fraction %28x%5E2-x-2%29%2F%28x%2B1%29.


%28%28%28x%2B5%29%28x-2%29%29%2F%28x%2B3%29%29%28%28x%2B1%29%2F%28x%5E2-x-2%29%29 Factor x%5E2%2B3x-10 to get %28x%2B5%29%2A%28x-2%29.


%28%28%28x%2B5%29%28x-2%29%29%2F%28x%2B3%29%29%28%28x%2B1%29%2F%28%28x%2B1%29%28x-2%29%29%29 Factor x%5E2-x-2 to get %28x%2B1%29%2A%28x-2%29.


%28%28x%2B5%29%28x-2%29%28x%2B1%29%29%2F%28%28x%2B3%29%28x%2B1%29%28x-2%29%29 Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


%28x%2B5%29%2F%28x%2B3%29 Simplify.


So %28%28x%5E2%2B3x-10%29%2F%28x%2B3%29%29%2F%28%28x%5E2-x-2%29%2F%28x%2B1%29%29 simplifies to %28x%2B5%29%2F%28x%2B3%29.


In other words, where x%3C%3E-3, x%3C%3E-1, or x%3C%3E2