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May 21st, 2015, 03:04 AM   #1
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Perform the division and do the answers as easy as possible

Task 1.33
D) (2x^2-4)/(x-1) : (2)/(x-1) = (2x^2-4*(x-1))/((x-1)*2)= (2(x^2-2) * (x-1) (x+1)) / ((x+1) (x-1) *2) = (2x^2 -2 * x^2 - 1^2)/(x^2 - 1^2 * 2)
I think what happens here is that the 2x-2 turns into 0x^2 which is x^2 and i think some of the letters and numbers get shorten. I think x^2 - - 1 ^2 get shorten and removed from the tasks in both sides. So that we end up with
(x^2)/(2) and then we change sides of 2 so that we get x^2 (-2) = x^2 -2.

Did i do this task correctly?
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May 21st, 2015, 05:35 AM   #2
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This is how I would do it:

$\displaystyle \frac{2x^2 - 4}{x-1} \div \frac{2}{x-1}$
$\displaystyle =\frac{2(x^2 - 2)}{x-1} \cdot \frac{x-1}{2}$
$\displaystyle =\frac{\cancel{2}(x^2 - 2)}{\cancel{x-1}} \cdot \frac{\cancel{x-1}}{\cancel{2}}$
$\displaystyle = x^2-2$
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