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Chapter 7: Problem 78

Explain how to divide rational expressions.

Short Answer

Expert verified
Dividing rational expressions is essentially changed to a multiplication operation. The procedure involves rewriting the division as multiplication of the first fraction and the reciprocal of the second fraction. Then, multiply the fractions together and simplify the resulting rational expression if possible.

Step by step solution

01

Rewrite the Division as Multiplication

Given a division of rational expressions in the form \(\frac{a}{b} 梅 \frac{c}{d}\), rewrite the division operation as multiplication by changing it to \(\frac{a}{b} * \frac{d}{c}\). This is based on the rule that \(\(a 梅 b = a * (1/b)\).
02

Find the Reciprocal of the Second Fraction

The reciprocal of a fraction is obtained by switching its numerator and denominator. Therefore, if the second fraction is \(\frac{c}{d}\), its reciprocal will be \(\frac{d}{c}\). So, replacing the divisor \(\frac{c}{d}\) with its reciprocal turns the division into multiplication, resulting in \(\frac{a}{b} * \frac{d}{c}\).
03

Multiply the Fractions

Now that you have two fractions, multiply them straight across (numerator with numerator and denominator with denominator). Thus, the expression becomes \((a*d) / (b*c)\).
04

Simplify the Resulting Fraction

If the resulting fraction \((a*d) / (b*c)\) can be further simplified by factoring and cancelling out common terms found in both numerator and denominator, do so. If not, then \((a*d) / (b*c)\) is the final answer and can't be simplified further.

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Most popular questions from this chapter

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