You can
put this solution on YOUR website!I interpret your problem as being asked to simplify:
Let's work on the denominator first. You may recognize is as "a" take away one-half "a".
The result is
If you didn't recognize that, a more general approach would be to say that to combine
fractions you need to have them over a common denominator. How would you combine
with
? One has a denominator and the other doesn't. What if you multiplied the
by
. [Since
is the same as
, you are effectively multiplying
by
so you are not really changing the
. You are just converting
the
to
.] In this form you now have a common form for the two terms in
the denominator of your problem. That denominator is:
Notice that these two terms have a common denominator of 2 so they can be combined.
Substituting this result into your problem results in your problem now being:
So you are dividing
by the fraction
}.
One way to look at this is to use the old arithmetic rule ... when you divide by a fraction,
you invert it and then multiply this inverted fraction times the number that you are dividing.
So, using that rule, we invert
to get
. Then we multiply that by
the
that is the original numerator of your problem.
The
in the denominator of this product cancels with the
in the numerator
to leave just
as the simplification of your original problem.
A way that you could do a reality check of your answer is to return to the original
problem and assign a value to
. For example, you might say that
is 1.
This would make your original problem:
Using "real" numbers may make it a little easier for you to see that the denominator
simplifies to
. Then ask yourself, "How many times does
go into
?" A little thought will tell you that there are 2 halves in
. So by using real numbers you have found that the problem reduces to 2. This helps
to confirm that our previous work was correct and that the original problem simplifies
to
Hope this helps.
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