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Chapter 0: Problem 90

Explain how to divide rational expressions.

Short Answer

Expert verified
In brief, to divide rational expressions, one needs to rewrite the division as a multiplication by taking the reciprocal of the divisor, simplify the expressions by factoring the polynomials, cancel out common factors, and then simplify the final result.

Step by step solution

01

Understand the Problem

Recognize that a rational expression is simply a fraction in which the numerator and/or the denominator are polynomials. Here, the given task is to divide one rational expression by another. The problem is how to do this in a systematic and correct way.
02

Rewrite The Division as Multiplication

The first step in dividing rational expressions is to write the division as a multiplication. To do this, take the reciprocal of the second fraction, i.e., interchange the numerator and the denominator of the second fraction. Now, the division problem will turn into a multiplication problem.
03

Factor Polynomials

Factor all the polynomials in the numerators and denominators of the two fractions if possible. Factoring polynomials is key to simplifying complex rational expressions.
04

Cancel out Common Factors

Check if there are any common factors in the numerators and denominators across the two fractions. If there are, you can cancel out these common factors. After cancelling out common factors, you can multiply the numerators together and the denominators together to form a single fraction which will be the final answer.
05

Simplify The Final Expression

The last step is to simplify the final rational expression obtained after multiplication. This can usually be done by combining like terms or further factoring and cancelling out.

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