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Chapter 0: Problem 100

Explain how to multiply rational expressions.

Short Answer

Expert verified
To multiply rational expressions, one must first factorize the numerators and denominators, then multiply the numerators together and the denominators together. Afterwards, simplify the resulting expression by cancelling out any common factors in the numerator and the denominator.

Step by step solution

01

Factorize Numerator and Denominator

The first step is to factorize the numerators and the denominator of both expressions. Factoring a polynomial means to break it up into the product of simpler polynomials.
02

Multiply Numerators and Denominators Separately

This step involves multiplying the numerators together to form a single numerator and doing the same for the denominators to form a single denominator for your new rational expression. This is like standard fraction multiplication where numerators are multiplied with numerators, and denominators with denominators.
03

Simplify the Expression

After multiplying, you can simplify the expression by cancelling out the common factors in the numerator and the denominator.

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Most popular questions from this chapter

Will help you prepare for the material covered in the first section of the next chapter. If \(y=4-x^{2},\) find the value of \(y\) that corresponds to values of \(x\) for each integer starting with -3 and ending with 3

Perform the indicated operations. Simplify the result, if possible. $$\left(\frac{1}{a^{3}-b^{3}} \cdot \frac{a c+a d-b c-b d}{1}\right)-\frac{c-d}{a^{2}+a b+b^{2}}$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The equation \(a x^{2}+c=0, a \neq 0,\) cannot be solved by the quadratic formula.

Will help you prepare for the material covered in the first section of the next chapter. If \(y=4-x,\) find the value of \(y\) that corresponds to values of \(x\) for each integer starting with -3 and ending with 3

Rationalize the numerator. $$\frac{\sqrt{x}+\sqrt{y}}{x^{2}-y^{2}}$$
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