SOLUTION: Please help me solve this equation: ((2x^2-8x-42)/(6x^2))/((x^2-9)/(x^2-3x))

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Question 243596: Please help me solve this equation: ((2x^2-8x-42)/(6x^2))/((x^2-9)/(x^2-3x))
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%282x%5E2-8x-42%29%2F%286x%5E2%29%29%2F%28%28x%5E2-9%29%2F%28x%5E2-3x%29%29 Start with the given expression.


%28%282x%5E2-8x-42%29%2F%286x%5E2%29%29%2A%28%28x%5E2-3x%29%2F%28x%5E2-9%29%29 Multiply the first fraction by the reciprocal of the second fraction.


%28%282%2A%28x%2B3%29%2A%28x-7%29%29%2F%286x%5E2%29%29%28%28x%5E2-3x%29%2F%28x%5E2-9%29%29 Factor 2x%5E2-8x-42 to get 2%2A%28x%2B3%29%2A%28x-7%29.


Factor 6x%5E2 to get 2%2A3%2Ax%2Ax.


Factor x%5E2-3x to get x%2A%28x-3%29.


Factor x%5E2-9 to get %28x-3%29%2A%28x%2B3%29.


%282%2Ax%2A%28x%2B3%29%2A%28x-7%29%28x-3%29%29%2F%282%2A3%2Ax%2Ax%28x-3%29%2A%28x%2B3%29%29 Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


%28x-7%29%2F%283x%29 Simplify.


So %28%282x%5E2-8x-42%29%2F%286x%5E2%29%29%2F%28%28x%5E2-9%29%2F%28x%5E2-3x%29%29 simplifies to %28x-7%29%2F%283x%29.


In other words,