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Chapter 7: Problem 18

Multiply as indicated. $$\left(y^{2}-16\right) \cdot \frac{3}{y-4}$$

Short Answer

Expert verified
The simplified form of the given expression is \(3(y + 4)\)

Step by step solution

01

Identify and factorize perfect squares

In this expression, \(y^{2}-16\) is a difference of squares as 16 is a perfect square. Difference of squares can be factorized as \((a+b)(a-b)\). So, \(y^{2} - 16\) can be factorized as \((y - 4)(y + 4)\).
02

Replace the original expression

Replace the expression \(y^{2}-16\) in the original expression with its factorized form which gives \((y - 4)(y + 4) \cdot \frac{3}{y - 4}\)
03

Simplify the expression

Here, we can directly cancel the same term \((y - 4)\) in the numerator and the denominator which results in \((y + 4) \cdot 3\).
04

Write the final result

Rearrange the expression to get the final form, which is \(3(y + 4)\).

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Most popular questions from this chapter

Explain how to add rational expressions when denominators are the same. Give an example with your explanation.

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{10}{x-2}-\frac{6}{2-x}$$

Will help you prepare for the material covered in the next section. a. If \(y=k x\) find the value of \(k\) using \(x=2\) and \(y=64\) b. Substitute the value for \(k\) into \(y=k x\) and write the resulting equation. c. Use the equation from part (b) to find \(y\) when \(x=5\)

use the GRAPH or TABLE feature of a graphing utility to determine if the subtraction has been performed correctly. If the answer is wrong, correct it and then verify your correction using the graphing utility. $$\frac{x^{2}+4 x+3}{x+2}-\frac{5 x+9}{x+2}=x-2, x \neq-2$$

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{5 x-2}{3 x-4}+\frac{2 x-3}{4-3 x}$$
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