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Chapter 7: Problem 13

Multiply as indicated. $$\frac{4 y+30}{y^{2}-3 y} \cdot \frac{y-3}{2 y+15}$$

Short Answer

Expert verified
The simplified multiplication of the given expressions is \( \frac{2}{y(y+5)} \)

Step by step solution

01

Factor the Fractions

Factor the given fractions. This gives \( \frac{2(2y+15)}{y(y-3)} \cdot \frac{y-3}{y+5} \)
02

Cancel terms

Upon factoring, you notice that (2y+15) and (y-3) are terms in both the numerator and the denominator. You can cancel them out, simplify if possible, and write the simplest form of the fractions.
03

Perform the Multiplication

After cancelling out like terms, the resulting fractions are \( \frac{2}{y} \cdot \frac{1}{y+5} \). Multiply the numerators and the denominators separately. Multiply 2 by 1 for the numerator, and y by (y+5) for the denominator. The multiplication yields \( \frac{2}{y(y+5)} \)

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Most popular questions from this chapter

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{6}{x-1}-\frac{5}{1-x}$$

Add or subtract as indicated. Simplify the result, if possible. $$\frac{3}{y+1}+\frac{2}{3 y}$$

The temperature, in degrees Fahrenheit, of a dessert placed in a freezer for \(t\) hours is modeled by $$ \frac{t+30}{t^{2}+4 t+1}-\frac{t-50}{t^{2}+4 t+1} $$ a. Express the temperature as a single rational expression. b. Use your rational expression from part (a) to find the temperature of the dessert, to the nearest hundredth of a degree, after 1 hour and after 2 hours.

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{3-x}{x-7}-\frac{2 x-5}{7-x}$$

Add or subtract as indicated. Simplify the result, if possible. $$\frac{2}{x}+9$$
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