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Chapter 7: Problem 5

Find all numbers for which each rational expression is undefined. If the rational expression is defined for all real numbers, so state. $$\frac{13}{5 x-20}$$

Short Answer

Expert verified
The rational expression \(\frac{13}{5x - 20}\) is undefined for \(x = 4\).

Step by step solution

01

Identify the denominator

In the rational expression \(\frac{13}{5x - 20}\), the denominator is \(5x - 20\).
02

Set the denominator equal to zero

To find the values of x which cause the denominator to become zero, and therefore undefined, set the denominator equal to zero: \(5x - 20 = 0\).
03

Solve for \(x\)

Solving the equation \(5x - 20 = 0\), gives \(x = \frac{20}{5}\) or \(x = 4\).

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Most popular questions from this chapter

Describe how to identify the corresponding sides in similar triangles.

Add or subtract as indicated. Simplify the result, if possible. $$\frac{7}{x}+4$$

Add or subtract as indicated. Simplify the result, if possible. $$\frac{2}{y+5}+\frac{3}{4 y}$$

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{3-x}{x-7}-\frac{2 x-5}{7-x}$$

perform the indicated operation or operations. Simplify the result, if possible. $$\frac{2 y}{y-5}-\left(\frac{2}{y-5}+\frac{y-2}{y-5}\right)$$
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