How do I solve this complex fraction
Algebra

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Thank you for the opportunity to help you with your question!
You have to work your way from the bottom fraction to the top fraction :)
The answer is:2a(5a7)/(7a10)
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 :)
How can I view how you got to that answer?
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 12/a. We need 1 to have a common denominator before we can subtract it.
(a/a)*1  2/a
a/a  2/a = a2/a.
Now we have:
2 + 1/(a2/a)
Anything divided by a fraction can be multiplied by the inverse of the fraction:
1/ (a2)/a = 1 * a/(a2) = a/(a2)
So now we have:
2 + a/(a2)
We need a common denominator:
(a2/a2)*2 + a/(a2) = 2a4/(a2) + a/a2. Combine the numerator now that the denominator is the same:
2a4+a/(a2) = 3a4/(a2).
So, let's state what we have now:
a + a/(2 + 1/(3a4/a2).
1/(3a4/a2) = a2/3a4
2 + (a2)/(3a4). We need a common denominator again:
(3a4)/(3a4) * 2 + (a2)/(3a4) = 6a  8/(3a4) + a2/(3a4) = (6a  8 + a  2) / (3a4)
Simplify:
(7a  10) / (3a4)
a + a/[(7a10)/(3a4)]
Again, anything divided by a fraction can be multiplied by its inverse:
a + a * (3a4)/(7a10) = a + a(3a4)/(7a10)
Multiply a to get the same denominator:
a*(7a10)/(7a10) = a(7a10)/(7a10) + a(3a4)/(7a10)
Combine:
[a(7a10) + a(3a4) ] / (7a10)
Simplify:
7a^2  10a + 3a^2  4a = 10a^2  14a = 2a(5a  7)/(7a  10)
And there you have it!
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