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Chapter 0: Problem 28

Multiply or divide as indicated. $$\frac{x^{2}+x}{x^{2}-4} \div \frac{x^{2}-1}{x^{2}+5 x+6}$$

Short Answer

Expert verified
The simplified fraction is \(\frac{x}{x - 1}\)

Step by step solution

01

Remember the division rule for fractions

The rule for dividing fractions is to multiply the first fraction by the reciprocal of the second one. In this case, it means flipping the second fraction and changing the division to multiplication.\[\frac{x^{2}+x}{x^{2}-4} \times \frac{x^{2}+5 x+6}{x^{2}-1}\]
02

Factor polynomials

Next, factor all of the polynomials in the numerators and denominators of both fractions: \[\frac{x*(x + 1)}{(x - 2)*(x + 2)} \times \frac{(x + 2) * (x + 3)}{(x - 1)*(x + 1)}\]
03

Simplify

Now simplify the equation by canceling out terms that appear in the numerator and the denominator. After simplifying the equation, only (x - 1) remains in the denominator and (x) remains in the numerator: \[\frac{x}{x - 1}\]

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Most popular questions from this chapter

Describe ways in which solving a linear inequality is similar to solving a linear equation.

Explain how to add rational expressions having no common factors in their denominators. Use \(\frac{3}{x+5}+\frac{7}{x+2}\) in your explanation.

What is a rational expression?

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. An elevator at a construction site has a maximum capacity of 3000 pounds. If the elevator operator weighs 245 pounds and each cement bag weighs 95 pounds, how many bags of cement can be safely lifted on the elevator in one trip?

Explain how to divide rational expressions.
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