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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