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Rational Expressions
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Simplification of rational expressions, reducing to lowest
terms
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Addition and subtraction of rational
expressions
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Simplification of rational expressions, reducing to lowest
terms
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A
rational expression is a fraction of which the numerator and the
denominator are polynomials. |
A
rational expression is reduced to lowest terms if all common
factors from the numerator and denominator are canceled. |
To
reduce a rational expression to lowest terms first factorize
both the numerator and denominator as much as possible then
cancel common factors, i.e., divide their numerator and
denominator by common factors. |
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Examples:
Reduce the following
rational expression to lowest terms. |
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factoring
out the minus sign, |
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or |
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Examples:
Reduce or simplify the following
rational expression to lowest terms. |
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Addition and subtraction of rational
expressions
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To add or subtract two fractions with
the same denominator, add or subtract the numerators and write the sum over the common denominator. |
To add or subtract fractions with different
denominators: |
First find
the least common denominator (lcd -the smallest number that can be
divided by each denominator). |
Write equivalent fractions using this
denominator. Then add or subtract the fractions. |
The
process for rational expressions is identical. |
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Examples:
Perform the indicated
operations and reduce the answer to lowest terms. |
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Note,
since each second line should be subtracted, the sign of each term is reversed. |
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Pre-calculus
contents A
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