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Chapter 0: Problem 31

Multiply or divide as indicated. $$\frac{x^{2}+x-12}{x^{2}+x-30} \cdot \frac{x^{2}+5 x+6}{x^{2}-2 x-3} \div \frac{x+3}{x^{2}+7 x+6}$$

Short Answer

Expert verified
The result is \(x+4 / x-5\).

Step by step solution

01

Factorize each expression

Factorize each quadratic expression involved in the exercise.\n\(\frac{{(x+4)(x-3)}}{{(x+6)(x-5)}} \cdot \frac{{(x+2)(x+3)}}{{(x+1)(x-3)}} \div \frac{{(x+3)}}{{(x+2)(x+3)}}\)
02

Rewrite the division as multiplication

Rewrite the division by \(\frac{{x+3}}{{x^{2}+7x+6}}\) as the multiplication by its reciprocal, \(\frac{{x^{2}+7x+6}}{{x+3}} = \frac{{(x+2)(x+3)}}{{x+3}}\).\nThen, the expression becomes \n\(\frac{{(x+4)(x-3)}}{{(x+6)(x-5)}} \cdot \frac{{(x+2)(x+3)}}{{(x+1)(x-3)}} \cdot \frac{{(x+2)(x+3)}}{{x+3}}.\)
03

Simplify

Simplify the expression by canceling out equivalent expressions that appear in the numerator and the denominator.\nAfter canceling, the expression becomes \((x+4)/(x-5)\).
04

Rewriting the result

The result may be rewritten without parentheses.\nThe result is \(x+4 / x-5\).

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Most popular questions from this chapter

Evaluate each algebraic expression for the given value or values of the variable(s). $$\frac{2 x+y}{x y-2 x}, \text { for } x=-2 \text { and } y=4$$

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