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Chapter 7: Problem 55

Which method do you prefer for simplifying complex rational expressions? Why?

Short Answer

Expert verified
The preferred method for simplifying complex rational expressions is by multiplying by the common denominator, as it converts division problems into simpler multiplication problems and makes the intermediate steps clearer.

Step by step solution

01

Identify the Preferred Method

One common method for simplifying complex rational expressions is by multiplying by the common denominator. This is a preferred method because it eliminates the fractions in the complex fraction, simplifying the expression.
02

Explain the Method

To use this method, factor all denominators to find the least common denominator (LCD). Then, multiply every term in the complex fraction (both numerator and denominator) by this LCD. This should result in fractions being eliminated, hence simplifying the expression.
03

Discuss the Reason Behind Preference

This method essentially turns a division problem into a multiplication problem, which many find easier to handle. It also makes the intermediate steps clearer, minimizing mistakes. Apart from this, having one uniform way to deal with these problems simplifies the process.

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Most popular questions from this chapter

perform the indicated operation or operations. Simplify the result, if possible. $$\frac{22 b+15}{12 b^{2}+52 b-9}+\frac{30 b-20}{12 b^{2}+52 b-9}-\frac{4-2 b}{12 b^{2}+52 b-9}$$

Factor: \(25 x^{2}-81 .\) (Section 6.4, Example 1)

Add or subtract as indicated. Simplify the result, if possible. $$\frac{3}{x}+\frac{4}{x-6}$$

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{2 x-y}{x-y}+\frac{x-2 y}{y-x}$$

perform the indicated operations. Simplify the result, if possible. $$\left(\frac{3 x^{2}-4 x+4}{3 x^{2}+7 x+2}-\frac{10 x+9}{3 x^{2}+7 x+2}\right) \div \frac{x-5}{x^{2}-4}$$
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