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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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Multiplication and division of rational
expressions
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Solving complex 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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| 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. |
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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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| Multiplication and division of rational
expressions
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| Use
the formulas for the multiplication
and the division of fractions. |
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and |
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| Notice
the two special cases of which should be aware of: |
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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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| Solving complex rational expressions
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| A complex or compound rational expression has fractional expressions in its numerator, denominator or both. |
| To simplify complex fractions, change the complex fraction into a division problem, i.e., divide the numerator by the denominator. |
| Examples:
Simplify complex
fractions. |
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| Intermediate
algebra contents |
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| Copyright
© 2004 - 2012, Nabla Ltd. All rights reserved. |
