How is doing operations—adding, subtracting, multiplying, and dividing—with rational expressions similar to or different from doing operations with fractions? Can understanding how to work with...

How is doing operations—adding, subtracting, multiplying, and dividing—with rational expressions similar to or different from doing operations with fractions? Can understanding how to work with one kind of problem help understand how to work another type? When might you use this skill in real life?

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llltkl | College Teacher | (Level 3) Valedictorian

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A rational expression is essentially a fraction,except that the numerator and denominator are polynomial expressions instead of integers. It is an expression that is the ratio of two polynomials.

Eg. `(x^2+5)/(x+2)` is a rational expression in the general form `f(x)=(P(x))/(Q(x))`

where Q(x) cannot be 0 because it is undefined.

The operations follow exactly the same rules, since rational expressions are fractions.

The steps are identical however, in rational functions (polynomials, expressions), we need to factor everything first.
For add or subtract:
step 1 - factor all that can be factored using your factoring steps.
step 2 - get a common denominator
step 3 - change your numerators
step 4 - combine like terms in the numerator
step 5 - factor the numerator
step 6 - reduce anything left over.
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For multiply
step 1 - factor all that can be factored using your factoring steps
step 2 - cancel anything in the top and bottom.
step 3 - multiply what is left in the top and what is left in the bottom to get your final answer.
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for divide
step 1 - factor all that can be factored using your factoring steps.
step 2 - multiply by the reciprocal of the second fraction.
step 3 - follow the multiplication steps.

You can even cancel common terms from the numerator and denominator like in numerical fractions. Manipulation of rational expressions is similar to manipulation of fractions.

First of all, school is real life. You might use this skill in "real life" when setting up a proportion and there is an unknown value. Scale drawings, for example. It is also used to add two ratios or may be variable probalities that depend on various factors.

 
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