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Chapter 0: Problem 30

Multiply or divide as indicated. $$\frac{x^{2}-4}{x^{2}+3 x-10} \div \frac{x^{2}+5 x+6}{x^{2}+8 x+15}$$

Short Answer

Expert verified
The simplified form of the given expression is \( \frac{(x-2)(x+5)}{(x-5)(x+2)} \).

Step by step solution

01

Rewriting the Divisor

Change the equation to multiplication by taking the reciprocal of the divisor. \[\frac{x^{2}-4}{x^{2}+3 x-10} \times \frac{x^{2}+8 x+15}{x^{2}+5 x+6}\]
02

Factorize

Factorize all the expressions. Doing this helps to simplify the expression. We get:\[\frac{(x-2)(x+2)}{(x-5)(x+2)} \times \frac{(x+3)(x+5)}{(x+2)(x+3)}\]
03

Simplify

Now cancel out common factors:\[\frac{(x-2)}{(x-5)} \times \frac{(x+5)}{(x+2)}\]
04

Multiply

Finally, multiply the remaining fractions:\[\frac{(x-2)(x+5)}{(x-5)(x+2)}\]This cannot be further simplified.

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Most popular questions from this chapter

List all numbers from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. $$\\{-7,-0 . \overline{6}, 0, \sqrt{49}, \sqrt{50}\\}$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Although \(20 x^{3}\) appears in both \(20 x^{3}+8 x^{2}\) and \(20 x^{3}+10 x\) I'll need to factor \(20 x^{3}\) in different ways to obtain each polynomial's factorization

Evaluate each algebraic expression for the given value or values of the variable(s). $$8 x-y, for\quad x=3\quad and\quad y=4$$

$$\text { factor completely.}$$ $$-x^{2}-4 x+5$$

$$\text { Factor completely.}$$ $$3 x^{2}+5 x y^{2}+2 y^{4}$$
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