Quadratic Equation - Why is this the answer?
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Please see the attached picture. I don't understand why crossing the respective numerators and denominators and multiplying the denominators doesn't work for this problem. For example, I know that a/b + c/d = (ad+bc)/bd. I tried using this method but did not get the correct answer. Please help me understand. Thank you!
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Hi Poisson,
If you take a good look at the first two 'lines' of your work, you'll see that you just removed the denominators from the calculation (and then you just combined the numerators) - that is NOT mathematically correct. If you want to approach this question algebraically, then that's your choice (although it will be a lot of work!), but you have to combine like terms before you 'cancel out' a fraction. You would likely find it MUCH faster to TEST VALUES (try TESTing A=2 or A=4 and track the results).
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Rich
If you take a good look at the first two 'lines' of your work, you'll see that you just removed the denominators from the calculation (and then you just combined the numerators) - that is NOT mathematically correct. If you want to approach this question algebraically, then that's your choice (although it will be a lot of work!), but you have to combine like terms before you 'cancel out' a fraction. You would likely find it MUCH faster to TEST VALUES (try TESTing A=2 or A=4 and track the results).
GMAT assassins aren't born, they're made,
Rich
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You were good up to the point where you combined the fraction, but then you cancelled terms that couldn't be cancelled. And where did the 0 come from? That expression does not equal zero. It equals one of the answer choices.Poisson wrote:Attached is a copy of my work. The answer is B but I got D and E using the shortcut for getting common denominators. Any help would be greatly appreciated.
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The correct way to approach this algebraically would be to factor out a -1 from the denominator of the second term as follows:
((a^2 + 12) / (a-3)) + (7a / (3-a)) = ((a^2 + 12) / (a-3)) + (7a / ((-1)(a-3))
Now the -1 can be freely moved to the numerator, so it simplifies as follows:
((a^2 + 12) / (a-3)) + (-7a / (a-3))
Now we have a common denominator and are able to add the numerators:
(a^2 - 7a + 12) / (a-3)
Factor the quadratic expression in the numerator:
(a-3)(a-4)/(a-3)
And cancel like terms.
The answer is a-4.
((a^2 + 12) / (a-3)) + (7a / (3-a)) = ((a^2 + 12) / (a-3)) + (7a / ((-1)(a-3))
Now the -1 can be freely moved to the numerator, so it simplifies as follows:
((a^2 + 12) / (a-3)) + (-7a / (a-3))
Now we have a common denominator and are able to add the numerators:
(a^2 - 7a + 12) / (a-3)
Factor the quadratic expression in the numerator:
(a-3)(a-4)/(a-3)
And cancel like terms.
The answer is a-4.
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Remember for all a & b, a - b = - (b - a). And (a-b)^2 = (b-a)^2, because squaring always produces a positive result and each of those expressions have the same absolute value.
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If a=0, then (a²+12)/(a-3) + 7a/(3-a) = (0+12)/(0-3) + 0 = -4.
Now plug a=0 into the answer choices to see which yields a result of -4.
Only B works:
a-4 = 0-4 = -4.
The correct answer is B.
Now plug a=0 into the answer choices to see which yields a result of -4.
Only B works:
a-4 = 0-4 = -4.
The correct answer is B.
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