# Adding and Subtracting Rational Expressions with Like Denominators

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and Subtracting Rational Expressions:
Examples
(page
2 of 3)

these examples, note how I do everything neatly and orderly. You should
model your homework after these exercises, to help minimize errors.

• Simplify the following:

have a common denominator, so I can just add. But I’ll use parentheses
on the numerators, to make sure I carry the "minus" through
the second parentheses. (A common mistake would be to take the "minus"
sign only onto the "3x"
and not onto the "
4".)

• Simplify the following:

have a common denominator, so I can just combine them as they are. But
the denominator is a quadratic, so I’ll want to factor the numerator
when I’m done, to check and see if anything cancels out.

As you can see, something
did cancel. You always need to remember this step: factor the denominator
and numerator (if possible) and check for common factors. By the way,
since I was able to cancel off the "x – 2" factor,
this eliminated a zero from the denominator. Depending on your book
and on your instructor, you may (or may not) need to account for this
change in the domain of the fraction.

you might not need the "for x not equal to 2"
part. If you’re not sure, ask now, before the test.

• Simplify the following:

First I have to convert
these fractions to the common denominator of 2x2.
(If you’re not sure about the common denominator, do the factor table,
as shown in the second example on the
previous
page
, to check.)
Then I’ll add and, if possible, cancel off common factors.

Note how I used parentheses
to keep my subtraction straight. I wanted to be sure to carry the "minus"
through properly, and the extra step with the parentheses is very helpful
for this. Nothing cancelled in this case, so the answer is:

It isn’t common that you
will be able to simplify a rational addition or subtraction problem, but
you should get in the habit of checking. I would bet good money that you’ll
have a problem that simplifies on the test.

• Simplify the following:

The two denominators
have no common factors, so the common denominator will be
(2x – 1)(x – 6).

The numerator doesn’t
factor, so there is no chance of anything cancelling off. It is customary
to leave the denominator factored like this, so, unless your instructor
says otherwise, don’t bother multiplying the denominator out. The answer
is:

• Simplify the following:

Don’t let this one throw
you. The denominator of the "2"
is just "
1",
so the common denominator will be the only other denominator of interest:
"
x + 2".

Nothing cancels, so the

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