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You have to work your way from the bottom fraction to the top fraction :)The answer is:
Please let me know if you need any clarification. I'm always happy to answer your questions.
Because this is an easy question, we only have 20 minutes to answer. I am now going to type up the "how" of how this is done, because while the problem is easy, it's very difficulty to format in only 20 minutes :)
First and foremost, this is just a series of multiplying a common denominator, combining terms, and then simplifying.
The very first fraction to simplify is 1-2/a. We need 1 to have a common denominator before we can subtract it.
(a/a)*1 - 2/a
a/a - 2/a = a-2/a.
Now we have:
2 + 1/(a-2/a)
Anything divided by a fraction can be multiplied by the inverse of the fraction:
1/ (a-2)/a = 1 * a/(a-2) = a/(a-2)
So now we have:
2 + a/(a-2)
We need a common denominator:
(a-2/a-2)*2 + a/(a-2) = 2a-4/(a-2) + a/a-2. Combine the numerator now that the denominator is the same:
2a-4+a/(a-2) = 3a-4/(a-2).
So, let's state what we have now:
a + a/(2 + 1/(3a-4/a-2).
1/(3a-4/a-2) = a-2/3a-4
2 + (a-2)/(3a-4). We need a common denominator again:
(3a-4)/(3a-4) * 2 + (a-2)/(3a-4) = 6a - 8/(3a-4) + a-2/(3a-4) = (6a - 8 + a - 2) / (3a-4)
(7a - 10) / (3a-4)
a + a/[(7a-10)/(3a-4)]
Again, anything divided by a fraction can be multiplied by its inverse:
a + a * (3a-4)/(7a-10) = a + a(3a-4)/(7a-10)
Multiply a to get the same denominator:
a*(7a-10)/(7a-10) = a(7a-10)/(7a-10) + a(3a-4)/(7a-10)
[a(7a-10) + a(3a-4) ] / (7a-10)
7a^2 - 10a + 3a^2 - 4a = 10a^2 - 14a = 2a(5a - 7)/(7a - 10)
And there you have it!
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