SOLUTION: a student was given the problem 4x^2-9 divided by 6x-9 ------- 4x^2+12x+9 He answer is 3(2x-3). Is it correct, wh

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Question 155251: a student was given the problem 4x^2-9 divided by 6x-9
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4x^2+12x+9
He answer is 3(2x-3). Is it correct, why. And if not how would you suggest he solve the problem?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%284x%5E2-9%29%2F%286x-9%29%29%2F%284x%5E2%2B12x%2B9%29 Start with the given expression


%28%284x%5E2-9%29%2F%286x-9%29%29%2F%28%284x%5E2%2B12x%2B9%29%2F1%29 Rewrite 4x%5E2%2B12x%2B9 as a fraction by adding a denominator of 1


%28%284x%5E2-9%29%2F%286x-9%29%29%2A%281%2F%284x%5E2%2B12x%2B9%29%29 Multiply the top-most fraction by the reciprocal of the bottom-most fraction


%28%28%282x%2B3%29%282x-3%29%29%2F%286x-9%29%29%2A%281%2F%284x%5E2%2B12x%2B9%29%29 Factor 4x%5E2-9 to get %282x%2B3%29%282x-3%29


%28%28%282x%2B3%29%282x-3%29%29%2F%283%282x-3%29%29%29%2A%281%2F%284x%5E2%2B12x%2B9%29%29 Factor 6x-9 to get 3%282x-3%29


Factor 4x%5E2%2B12x%2B9 to get %282x%2B3%29%282x%2B3%29



%28%282x%2B3%29%282x-3%29%29%2F%283%282x-3%29%282x%2B3%29%282x%2B3%29%29 Combine the fractions


Highlight the common terms


Cancel out the common terms


1%2F%283%282x%2B3%29%29 Simplify


So %28%284x%5E2-9%29%2F%286x-9%29%29%2F%284x%5E2%2B12x%2B9%29 simplifies to 1%2F%283%282x%2B3%29%29


In other words, %28%284x%5E2-9%29%2F%286x-9%29%29%2F%284x%5E2%2B12x%2B9%29=1%2F%283%282x%2B3%29%29 where x%3C%3E-3%2F2 or x%3C%3E3%2F2


So his answer is incorrect. In the future, I would suggest checking the answer. You can check the answer by graphing the original expression and comparing it to the graph of the answer.