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Chapter 7: Problem 23

Multiply as indicated. $$\frac{x^{2}+6 x+9}{x^{3}+27} \cdot \frac{1}{x+3}$$

Short Answer

Expert verified
\( \frac{(x+3)}{(x^2-3x+9)} \)

Step by step solution

01

Factorize the Polynomials

To approach this problem, first factorize the expressions if possible. \n For the numerator of the first fraction \(x^{2}+6x+9\) and the denominator of the second fraction \(x^{3}+27\) can be factorized as \((x+3)^2\) and \((x+3)(x^2-3x+9)\) respectively.
02

Write each fraction with the factorized polynomials

Having factorized the polynomials, rewrite each fraction as follows: \(\frac{(x+3)^2}{(x+3)(x^2-3x+9)} \cdot \frac{1}{x+3}\)
03

Simplify the multiplication

Now simplify the multiplication by canceling out the common factor in the numerator and the denominator of the product if there is any. In this case, we have \(x+3\) common in the expressions, so we'll cancel one out which leaves the desired product as: \(\frac{(x+3)}{(x^2-3x+9)}\)

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Most popular questions from this chapter

add or subtract as indicated. Simplify the result, if possible. $$\begin{aligned} &\frac{x^{2}+9 x}{4 x^{2}-11 x-3}+\frac{3 x-5 x^{2}}{4 x^{2}-11 x-3}\\\ &x^{2}-4 x-4 x-4 \end{aligned}$$

Add or subtract as indicated. Simplify the result, if possible. $$\frac{3}{x-2}+\frac{4}{x+3}$$

add or subtract as indicated. Simplify the result, if possible. $$\frac{6 y^{2}+y}{2 y^{2}-9 y+9}-\frac{2 y+9}{2 y^{2}-9 y+9}-\frac{4 y-3}{2 y^{2}-9 y+9}$$

perform the indicated operation or operations. Simplify the result, if possible. $$\frac{y}{a x+b x-a y-b y}-\frac{x}{a x+b x-a y-b y}$$

Use a proportion to solve each problem. According to the authors of Number Freaking, in a global village of 200 people, 9 get drunk every day. How many of the world's 6.9 billion people \((2010\) population) get drunk everyday? Round to the nearest hundredth of a billion.
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