SOLUTION: how to simplify fully: 3x^2-75 ----------- 4x^2-17x-15 The ^2 means squared

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Question 230540: how to simplify fully:
3x^2-75
-----------
4x^2-17x-15

The ^2 means squared
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
To simplify/reduce any fraction, cancel common factors. And to do this we have to have factors. So we start by factoring:
%283x%5E2-75%29%2F%284x%5E2-17x-15%29
%283%28x%5E2-25%29%29%2F%28%284x+%2B+3%29%28x-5%29%29
%283%28x%2B5%29%28x-5%29%29%2F%28%284x+%2B+3%29%28x-5%29%29
Now that it's factored, we can see that there is a common factor, (x-5), which we can cancel:
%283%28x%2B5%29cross%28%28x-5%29%29%29%2F%28%284x+%2B+3%29cross%28%28x-5%29%29%29
leaving:
%283%28x%2B5%29%29%2F%284x+%2B+3%29
Nothing else cancels. (Note: The 3's do not cancel. The one on top is a factor but the one one the bottom is not.)
All that is left is to multiply out the numerator:
%283x%2B15%29%2F%284x+%2B+3%29