SOLUTION: A student was given the following problem: 4x^2 -9/4x^2 +12x + 9 divided by 6x -9 . He states his answer to the problem as 3(2x -3). Is he correct? If not, explain why. What would

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Question 156570: A student was given the following problem: 4x^2 -9/4x^2 +12x + 9 divided by 6x -9 . He states his answer to the problem as 3(2x -3). Is he correct? If not, explain why. What would you suggest he do to solve the problem?

Found 2 solutions by Edwin McCravy, gonzo:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
%284x%5E2+-9%29%2F%284x%5E2+%2B12x+%2B+9%29÷6x+-9

Write the 6x-9 as %286x-9%29%2F1

%284x%5E2+-9%29%2F%284x%5E2+%2B12x+%2B+9%29÷%286x+-9%29%2F1

Invert the second fraction and change the division
to multiplication:

%284x%5E2+-9%29%2F%284x%5E2+%2B12x+%2B+9%29×1%2F%286x+-9%29

Now factor 4x%5E2-9 as %282x-3%29%282x%2B3%29.
Factor 4x%5E2%2B12x%2B9 as %282x%2B3%29%282x%2B3%29
Factor 6x-9 as 3%282x-3%29

and replace the numerators and denominatore by
their factored forms:

%28%282x-3%29%282x%2B3%29%29%2F%28%282x%2B3%29%282x%2B3%29%29×1%2F%283%282x+-3%29%29

Indicate the multiplication of numerators and denominators,
so that we have just one fraction:

%28%282x-3%29%282x%2B3%29%2A1%29%2F%28%282x%2B3%29%282x%2B3%293%282x+-3%29%29

Cancel the %282x-3%29's



Cancel the %282x%2B3%29 in the top with one of the 
%282x%2B3%29's in the bottom:



All that's left is 

1%2F%28%282x%2B3%29%2A3%29

or

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

You can leave it like that, or distribute
out the bottom:

1%2F%286x%2B9%29

Edwin

Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
my solution looks a little different - here's why.................
4x^2 - 9 / 4x^2+12x+9 / 6x-9
=
4x^2-9 / (4x^2+12x+9 * 6x-9)
because a/b/c = (a/b) * (1/c) = a/(b*c)
factoring we get...............
(2x-3) * (2x+3) / ( (2x+3) * (2x+3) * 3 * (2x-3) )
dividing out like terms we get ................
1 / ( (2x+3) * 3 )
because one (2x-3) on top cancels out one (2x-3) on bottom and one (2x+3) on top cancels out one (2x+3) on bottom.
so the answer appears to be 1 divided by (2x+3)*3.