Problem 20 Multiply or divide as indicated.... [FREE SOLUTION]

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College Algebra

Robert Blitzer

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 0: Problem 20

Multiply or divide as indicated. $$\frac{x^{2}+5 x+6}{x^{2}+x-6} \cdot \frac{x^{2}-9}{x^{2}-x-6}$$

Short Answer

Expert verified

\[\frac{x^{2} - x - 6}{x - 2}\]

Step by step solution

Factoring Each Polynomial

To simplify the complex fractions, factor each polynomial as follows:\[\frac{x^{2}+5 x+6}{x^{2}+x-6} \cdot \frac{x^{2}-9}{x^{2}-x-6}\]can be factored into:\[\frac{(x + 2)(x + 3)}{(x - 2)(x + 3)} \cdot \frac{(x + 3)(x - 3)}{(x - 2)(x + 3)}\]

Simplifying The Expression

After factoring, cancel out the common factors in both the numerators and denominator:\[\frac{(x + 2)(x + 3)}{(x - 2)(x + 3)} \cdot \frac{(x + 3)(x - 3)}{(x - 2)(x + 3)}\]simplifies into:\[\frac{x + 2}{x - 2} \cdot \frac{x - 3}{1}\]

Multiplying The Fractions

Next, multiply across the numerators and the denominators:\[\frac{x + 2}{x - 2} \cdot \frac{x - 3}{1}\]gives:\[\frac{(x + 2) \cdot (x - 3)}{(x - 2) \cdot 1}\]

Simplifying The Result

Lastly, simplify the result of multiplication as follows:\[\frac{(x + 2)(x - 3)}{(x - 2)}\]gives the final simplified form of:\[\frac{x^{2} - x - 6}{x - 2}\]

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91影视

Multiply or divide as indicated. $$\frac{x^{2}+5 x+6}{x^{2}+x-6} \cdot \frac{x^{2}-9}{x^{2}-x-6}$$

Short Answer

Step by step solution

Factoring Each Polynomial

Simplifying The Expression

Multiplying The Fractions

Simplifying The Result

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