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Chapter 7: Problem 20

Find all numbers for which each rational expression is undefined. If the rational expression is defined for all real numbers, so state. $$\frac{8}{x^{2}+4}$$

Short Answer

Expert verified
The expression \(\frac{8}{x^{2}+4}\) is defined for all real numbers of \(x\).

Step by step solution

01

Set the denominator equal to zero

Start by setting the denominator of the rational expression \(x^{2}+4\) equal to zero and solve for \(x\). So, \(x^{2}+4 = 0\).
02

Solve for x

To solve for \(x\), you need to subtract 4 from both sides.\nThe equation becomes \(x^{2} = -4\)
03

Take the square root of both sides

Taking the square root of both sides to solve for \(x\), keep in mind that the square root of a negative number is not a real number. So, there are no real solutions to this equation. Therefore, the original rational expression is defined for all real numbers of \(x\).

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Most popular questions from this chapter

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{x^{2}}{x-3}+\frac{9}{3-x}$$

Factor: \(25 x^{2}-81 .\) (Section 6.4, Example 1)

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{5 x-2}{3 x-4}+\frac{2 x-3}{4-3 x}$$

Graph: \(y=-\frac{2}{3} x+4 .\) (Section 3.4, Example 3)

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