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The first thing we need to do on this problem is we need to
factor the denominators of all four of those fractions.
So V + 4 * V + 7 V -2 V plus 4V minus two V + 7 and V + 3 V +7.
So when we look at just the numerator, just the top part,
the common denominator here is going to be the V plus fours
because they're in common, but also the V + 7 and the V -, 2.
When I get that as my common denominator, I realized the
first term needed to get multiplied top and bottom by v
-, 2.
When I look at the second term, I realized the top and bottom
needed multiplied by v + 7, getting a common denominator.
For the denominator portion, the V + 7 is in common, but we need
the V - 2 and also the V + 3.
So this first term needed to multiply top and bottom by v +
3.
The second term needed to multiply top and bottom by v -,
2.
Once the denominators are the same, we combine the numerators.
So in the top we get V - 2 + V + 7 or two V + 5.
In the bottom we get V + 3 + V - 2 or two V + 1.
Once we have it as a fraction, we're going to realize that two
V + 5 doesn't have anything in common, so we can factor out of
12V.
Plus one doesn't have anything in common, so once again we can
factor out of one.
Instead of divining, we're going to take the reciprocal of the
bottom and multiply.
So the V -, 2 on top and bottom will cancel and the V + 7 on top
and bottom will cancel, leaving us two v + 5 * v + 3 / v + 4 * 2
V plus one.