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Chapter 0: Problem 73

Explain how to multiply rational expressions.

Short Answer

Expert verified
To multiply rational expressions, first multiply the numerators together and the denominators together to form a new rational expression. Then break down the resulting numerator and denominator into their factors. Finally, simplify the expression by canceling out any common factors in the numerator and the denominator.

Step by step solution

01

Multiplication of the Numerators and Denominators

The first step is to multiply the numerators (the top part of each fraction) together and the denominators (the bottom part of each fraction) together. You treat them separately, and you don't cross-multiply. This will result in a new rational expression.
02

Factorization

In this step, factorize the numerator and the denominator of the resulting rational expression. Factoring is the process of breaking down the given expressions into 'factor' terms which, when multiplied together, give the original expression.
03

Simplification

The last step involves simplifying the rational expression. Cancel out any common factors in the numerator and the denominator. Be careful not to cancel out terms - you can only cancel factors.

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Most popular questions from this chapter

In Exercises \(11-16,\) factor by grouping. $$3 x^{3}-2 x^{2}-6 x+4$$

Find all numbers that must be excluded from the domain of each rational expression. $$ \frac{7}{x-3} $$

state the name of the property illustrated. $$ 2(-8+6)=-16+12 $$

Simplify each exponential expression $$ \left(\frac{3 a^{-5} b^{2}}{12 a^{3} b^{-4}}\right)^{0} $$

state the name of the property illustrated. $$ \frac{1}{(x+3)}(x+3)=1, x \neq-3 $$
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