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Chapter 7: Problem 96

Explain how to simplify a rational expression with opposite factors in the numerator and denominator.

Short Answer

Expert verified
To simplify a rational expression with opposite factors in the numerator and denominator, identify any shared factors between the top and bottom of the fraction, and 'cancel' them out to simplify the ratio. The result is your simplified rational expression.

Step by step solution

01

Identify Common Factors

Firstly, it is important to identify any common factors that appear both in the numerator and the denominator of the rational expression.
02

Rule of Division

According to the rules of algebra, any factor divided by itself equals 1. Therefore, when the same factor appears in both the numerator and the denominator of a fraction, they can be 'cancelled out' or divided by each other to simplify the ratio.
03

Simplify the Expression

After identifying and cancelling all the common factors, the remaining terms in the numerator and denominator simplify the expression. There might be a need to further simplify the resulting expression by gathering like terms or using other arithmetic properties, but that's determined by the given expression.

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Most popular questions from this chapter

Will help you prepare for the material covered in the next section. If \(B=k W,\) find the value of \(k,\) in decimal form, using \(B=5\) and \(W=160\)

perform the indicated operation or operations. Simplify the result, if possible. $$\frac{y}{a x+b x-a y-b y}-\frac{x}{a x+b x-a y-b y}$$

perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\text { Simplify: } \frac{(y+2) y-2 \cdot 4}{4 y(y+4)}$$

A snowstorm causes a bus driver to decrease the usual average rate along a 60 -mile route by 15 miles per hour. As a result, the bus takes two hours longer than usual to complete the route. At what average rate does the bus usually cover the 60 -mile route?

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{9 x-1}{7 x-3}+\frac{6 x-2}{3-7 x}$$
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