##### How do I solve this complex fraction

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Oct 14th, 2015

You have to work your way from the bottom fraction to the top fraction :)

2a(5a-7)/(7a-10)

Oct 14th, 2015

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 :)

Oct 14th, 2015

How can I view how you got to that answer?

Oct 14th, 2015

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)

Simplify:

(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)

Combine:

[a(7a-10) + a(3a-4) ] / (7a-10)

Simplify:

7a^2 - 10a + 3a^2 - 4a = 10a^2 - 14a = 2a(5a - 7)/(7a - 10)

And there you have it!

Oct 14th, 2015

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Oct 14th, 2015
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Oct 14th, 2015
Oct 24th, 2017
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