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Chapter 0: Problem 89

Explain how to multiply rational expressions.

Short Answer

Expert verified
Multiplying rational expressions involves simplifying the expressions before multiplication, performing the multiplication like in fractions by multiplying numerators together and denominators together, and simplifying the final result if possible by removing common factors from the numerator and denominator.

Step by step solution

01

Simplify the Rational Expressions

First step in multiplying rational expressions requires simplifying each of the rational expressions individually -if possible-. This can be done by factoring the polynomials in the numerator and the denominator.
02

Perform the Multiplication

Multiplying rational expressions is the same as multiplying fractions. To multiply two fractions, multiply the numerators together for the new numerator, and the denominators together for the new denominator. Do the same for the rational expressions.
03

Simplify the Result

After the multiplication has been performed, the new rational expression may be able to be simplified further. Like with numbers, if the numerator and the denominator of the fraction have common factors, they can be divided to simplify the expression

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Most popular questions from this chapter

This will help you prepare for the material covered in the next section. a. Use a calculator to approximate \(\sqrt{300}\) to two decimal places. b. Use a calculator to approximate \(10 \sqrt{3}\) to two decimal places. c. Based on your answers to parts (a) and (b), what can you conclude?

Find the union of the sets. $$\\{1,3,5,7\\} \cup\\{2,4,6,8,10\\}$$

Factor the numerator and the denominator. Then simplify by dividing out the common factor in the numerator and the denominator. $$\frac{x^{2}+6 x+5}{x^{2}-25}$$

$$\text { factor completely.}$$ $$(x-5)^{-\frac{1}{2}}(x+5)^{-\frac{1}{2}}-(x+5)^{\frac{1}{2}}(x-5)^{-\frac{3}{2}}$$

$$\text { Factor completely.}$$ $$7 x^{4}+34 x^{2}-5$$
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