**Answer:**

Our restriction here is that the denominator of
a fraction can never be equal to 0. So, to find our domain, we want
to set the denominator "not equal" to 0 to restrict those values.

**Our domain is all real numbers except -9 and 9**, because they
both make the denominator equal to 0, which would not give us a real number
answer for our function.

**Answer:**

**Answer:**

**Answer:**

**Step 1: Find the LCD if needed.**

The **first denominator **has the following factor:

The **second denominator,** 3 - *x,* looks
like the first denominator except the signs are switched. We
can rewrite this as

**Putting all the different factors together and using the highest
exponent, we get the following LCD: **

**Step 2: Write equivalent fractions using the LCD if
needed.**

Now the two fractions have a common denominator, so we do not have to
rewrite the rational expressions.

**Step 3: Combine the rational expressions**

**AND **

**Step 4: Reduce to lowest terms.**

**Answer:**

**Step 1: Find the LCD if needed.**

The** first denominator** has the following two factors:

The **second denominator** has the following factor:

The **third denominator** has the following factor:

**Putting all the different factors together and using the highest
exponent, we get the following LCD: **

**Step 2: Write equivalent fractions using the LCD if
needed.**

Since the **first rational expression **already has the LCD, then
we do not need to change this fraction.

Rewriting the** second expression **with the LCD:

Rewriting the** third expression** with the LCD:

**Step 3: Combine the rational expressions**

**AND **

**Step 4: Reduce to lowest terms.**

**Answer:**

Note that I used method I described in Tutorial 34 (Complex Fractions) to work this problem. It is perfectly find to use method II here.

**Step 1: If needed, rewrite the numerator
and denominator so that they are each a single fraction**

**AND**

**Step 2: Divide the numerator by the denominator
by multiplying the numerator by the reciprocal of the denominator**

**AND**

**Step 3: If needed, simplify the rational expression.**

**Answer:**

Note that I used method II described in Tutorial 34: Complex Fractions to work this problem. It is perfectly fine to use method I here.

**Rewriting it with positive exponents we get:**

**Step 1: Multiply the numerator and denominator of the
overall complex fractions by the LCD of the smaller fractions**

**AND**

**Step 2: If needed, simplify the rational expression.**

The two **denominators of the numerator's fractions **have the
following factors: *a* and *b*

The two **denominators of the denominator's fractions ** have
the following factors: and

Putting all the different factors together and using the highest exponent
we get **the following LCD** for all the small fractions:

**Multiplying numerator and denominator by the LCD and simplifying
we get:**

**Answer:**

**Answer:**

**Step 1: Set up the long division **

**AND**

**Step 2: Divide 1st term of divisor by first term of
dividend to get first term of the quotient**

**AND**

**Step 3: Take the term found in step 1 and multiply
it times the divisor**

**AND**

**Step 4: Subtract this from the line above**

**AND**

**Step 5: Repeat until done**

**AND**

**Step 6: Write out the answer.**

**Final answer: **

Last revised on July 17, 2011 by Kim Seward.

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