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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
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# Rational Expressions

Simplifying Rational Expressions
To simplify a rational expression means to reduce it to lowest terms. From working with fractions, you may
recall that simplifying is done by cancelling common factors. Therefore, the key to simplifying rational
expressions (and to most problems involving rational expressions) is to factor the polynomials whenever
possible.
Example 1: Write in reduced form.

Solution: Factor the numbers and cancel common factors. Use properties of exponents to help cancel
the x’s:

Example 2: Write in reduced form.

Solution:

Question: Why is y ≠±2?
Answer: In order for our answer to be equivalent to the original fraction, the variable must have the
same restrictions. Since y cannot equal ±2 in the original expression (the denominator would then be zero), we
must restrict the domain of our answer in order for these fractions to be equivalent.

Example 3: Write in reduced form.

Solution:

At this point, it doesn’t look like anything will cancel. However, if we factor -1 from the last term in the
numerator, we obtain the following:

Question: What property of real numbers tells us that ?