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Exhibiting Rational Expressions

(1) Explain how multiplying and dividing rational expressions is similar to multiplication and division of fractions. Give an example of each and compare the process.

(2) When simplifying the rational expression (x+8)/(x+2), explain why it is improper to cancel out the x's. State a general rule for canceling factors in a rational expression and give an example of how this rule would be used.

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Solution Preview

(1) Each rational expression has the form

p(x)
------- , where p(x) and q(x) are polynomials. To multiply two rational expressions
q(x)

p(x) s(x)
-------- and ---------, we multiply their numerators and denominators separately:
q(x) t(x)

p(x) s(x) p(x)s(x)
-------- . ---------, = --------------
q(x) t(x) q(x)t(x)

To divide two rational expressions,

p(x) s(x)
-------- / ---------, we flip the second one and multiply the resulting expressions:
q(x) t(x)

p(x) s(x) p(x) t(x) p(x)t(x)
-------- / --------- = --------- . ---------- = ...

Solution Summary

Rational Expressions are exhibited.

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