SOLUTION: Solve the equation: y^2 - 3y - 18 over y^2 - 4 divided by y^2 + 5y + 6 over y - 2

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Question 109200: Solve the equation:
y^2 - 3y - 18 over y^2 - 4 divided by y^2 + 5y + 6 over y - 2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28y%5E2-3y-18%29%2F%28y%5E2-4%29%29%2F%28%28y%5E2%2B5y%2B6%29%2F%28y-2%29%29 Start with the given expression


%28%28y%5E2-3y-18%29%2F%28y%5E2-4%29%29%2A%28%28y-2%29%2F%28y%5E2%2B5y%2B6%29%29 Multiply the first fraction by the reciprocal of the second fraction


%28%28%28y-6%29%28y%2B3%29%29%2F%28y%5E2-4%29%29%2A%28%28y-2%29%2F%28y%5E2%2B5y%2B6%29%29 Factor y%5E2-3y-18 to get %28y-6%29%28y%2B3%29 (note: if you need help with factoring, check out this solver)

Factor y%5E2-4 to get %28y-2%29%28y%2B2%29


Factor y%5E2%2B5y%2B6 to get %28y%2B3%29%28y%2B2%29


Cancel like terms


%28y-6%29%2F%28%28y%2B2%29%28y%2B2%29%29 Simplify


%28y-6%29%2F%28y%2B2%29%5E2 Collect like terms


So %28%28y%5E2-3y-18%29%2F%28y%5E2-4%29%29%2F%28%28y%5E2%2B5y%2B6%29%2F%28y-2%29%29 simplifies to %28y-6%29%2F%28y%2B2%29%5E2