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Chapter 7: Problem 10

Multiply as indicated. $$\frac{x^{2}+9 x+18}{x+6} \cdot \frac{1}{x+3}$$

Short Answer

Expert verified
The result of the multiplication of the given expressions is 1.

Step by step solution

01

Simplification

Rewrite the given expression and simplify it, if it is possible. In this case, one can simplify the numerator of the first fraction. The expression \(x^{2}+9x+18\) can be factored into \((x+3)(x+6)\). By substitifying it then the new expression becomes \(\frac{(x+3)(x+6)}{x+6}\cdot\frac{1}{x+3}\).
02

Simplify the Expression

The rule of multiplication for fractions allows us to simplify them before multiplying. We can do this by canceling out common variables and constants from the numerator and the denominator. Here, (x+6) can be cancelled from both the numerator and denominator of the first fraction and (x+3) can be cancelled from the numerator of the first fraction and the denominator of the second fraction. Doing this, the expression becomes 1.
03

Conclusion

Since there's nothing more to be simplified, our final answer is 1.

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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.

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I can solve \(\frac{x}{9}=\frac{4}{6}\) by using the cross-products principle or by multiplying both sides by \(18,\) the least common denominator.

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. $$\frac{x^{2}-13}{x+4}-\frac{3}{x+4}=x+4, x \neq-4$$

add or subtract as indicated. Simplify the result, if possible. $$\frac{3 y^{2}-2}{3 y^{2}+10 y-8}-\frac{y+10}{3 y^{2}+10 y-8}-\frac{y^{2}-6 y}{3 y^{2}+10 y-8}$$

Will help you prepare for the material covered in the next section. a. If \(y=\frac{k}{x},\) find the value of \(k\) using \(x=8\) and \(y=12\) b. Substitute the value for \(k\) into \(y=\frac{k}{x}\) and write the resulting equation. c. Use the equation from part (b) to find \(y\) when \(x=3\)
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