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Chapter 0: Problem 99

Factor and simplify each algebraic expression. $$(x+5)^{-\frac{1}{2}}-(x+5)^{-\frac{3}{2}}$$

Short Answer

Expert verified
The simplified and factored form of the given algebraic expression is \( (x+5)^{-\frac{1}{2}} \times (-x-4) \)

Step by step solution

01

Identify Common Factor

Looking at the given expression, the common factor is \( (x+5)^{-\frac{1}{2}} \).
02

Factor out Common Base

Factor out the common base \( (x+5)^{-\frac{1}{2}} \), yielding: \( (x+5)^{-\frac{1}{2}} \times (1 - (x+5)) \).
03

Simplify the Resulting Expression

Simplify the second part of the expression \( 1 - (x+5) \) to yield \( -x-4 \). The final expression is then \( (x+5)^{-\frac{1}{2}} \times (-x-4) \)

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I can check inequalities by substituting 0 for the variable: When 0 belongs to the solution set, I should obtain a true statement, and when 0 does not belong to the solution set. I should obtain a false statement.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The equation \(a x^{2}+c=0, a \neq 0,\) cannot be solved by the quadratic formula.

Perform the indicated operations. Simplify the result, if possible. $$\left(2-\frac{6}{x+1}\right)\left(1+\frac{3}{x-2}\right)$$

Will help you prepare for the material covered in the first section of the next chapter. If \(y=|x+1|,\) find the value of \(y\) that corresponds to values of \(x\) for each integer starting with -4 and ending with 2

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. On two examinations, you have grades of 86 and \(88 .\) There is an optional final examination, which counts as one grade. You decide to take the final in order to get a course grade of A, meaning a final average of at least 90 . a. What must you get on the final to earn an A in the course? b. By taking the final, if you do poorly, you might risk the B that you have in the course based on the first two exam grades. If your final average is less than \(80,\) you will lose your \(\mathrm{B}\) in the course. Describe the grades on the final that will cause this to happen.
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