SOLUTION: can you please help me with: {{{4/(a-5)-1/(5-a)}}}

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Question 152501This question is from textbook Algebra structure and method book 1
: can you please help me with: 4%2F%28a-5%29-1%2F%285-a%29 This question is from textbook Algebra structure and method book 1

Answer by Edwin McCravy(20062) About Me  (Show Source):
You can put this solution on YOUR website!

4%2F%28a-5%29-1%2F%285-a%29

Notice that you have denominators
a-5 and 5-a. These are
called "reversed differences".

This is how we treat this: Take the
one which is not in descending order
5-a

write it in descending order:

-a%2B5

factor out -1, which changes
both signs:

-1%28a-5%29

or just -%28a-5%29

Now substitute that for5-a:

4%2F%28a-5%29-1%2F%28-%28a-5%29%29

Cancel the negative sign on the
bottom of the second fraction with
the minus sign in front of the
second fraction,making it a plus
in front of the second fraction:

4%2F%28a-5%29%2B1%2F%28a-5%29

Now the denominators are the same,
so all we need do is combine the
two numerators over their common
denominator:

%284%2B1%29%2F%28a-5%29

or

5%2F%28a-5%29

Edwin