For a review on working with expressions, including simplifying, adding, subtracting,
multiplying, dividing, and domains, see the Refresher Sections at the bottom of the Topic Page.

In Algebra 2, your work with rational expressions will be expanded.
Let's take a look at some of the types of problems you may be solving.

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ex1
Rewrite the expression ratsimp21 in keeping with ratsimp22where a(x), b(x), q(x) and r(x) are polynomials and the
degree of r(x) is less than the degree of b(x).

Answer:
This problem is asking you to divide the numerator by the denominator, and to write the answer as a quotient with a remainder.

You know how to accomplish this division, but perhaps you have not seen the question asked in this manner.

Note that this expression is undefined for the x-value of -3/2.


ratsimp23

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ex2
Explain if the simplification shown below is true, and whether there are any restrictions placed on the value of m:    ratsimp244

Answer:
This simplification is true since a value divided by itself equals one.

Yes, there are restrictions on m.
m ≠ -6 and m ≠ 3. Notice that when the second fraction is inverted, (x - 3) becomes a denominator which cannot be zero.

ratsimp5

m ≠ -6 and m ≠ 3.


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ex3
Show that the following statement is true.   ratsimp26

Answer:
When "showing" that a statement is true, be sure to include sufficient information to demonstrate that you understand what is happening, and why, in the problem.

Also, comment on the stated restriction.

By long division, it can be seen that the quotient is 1 and the remainder is 1.simprat27
When the remainder is expressed over the divisor, the given statement is shown to be true. The restriction of x ≠ -2 is needed to prevent a zero denominator.
simprat28

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ex4
Combine and simplify:  simprat29. Specify restriction(s).

Answer:
Factor where possible.

Find the common denominator for the three denominators, which is 2x(x - 7).

Adjust the numerators to accommodate the new denominators. Add and subtract.

Then simplify.

Be sure to include restrictions that would apply to all of the three initial fractions.
simprat30

Restrictions: x ≠ 0, x ≠ 7

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ex5
Combine and simplify: simprat31. Specify restriction(s).

Answer:
Factor where possible.

Invert the term to be divided.

Reduce (and cancel) top expressions with bottom expressions.

Specify restrictions based upon the initial fractions and the inverted division fraction.

simprat32

Restrictions: x ≠ 0, x ≠ ±3, x ≠ 2, x ≠ -5



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