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Chapter 7: Problem 6

Find all numbers for which each rational expression is undefined. If the rational expression is defined for all real numbers, so state. $$\frac{17}{6 x-30}$$

Short Answer

Expert verified
The rational expression is undefined when \(x = 5\).

Step by step solution

01

Identify when the denominator equals zero

The first step involves identifying when the denominator of the rational expression becomes zero, which is found by solving the equation \(6x - 30 = 0\) for \(x.\)
02

Solve the equation for \(x\)

To solve \(6x - 30 = 0\), first add 30 to both sides to isolate \(6x\) on the left side of the equation, which gives \(6x = 30\). Second, to find \(x\), divide each side by 6, resulting in \(x = 5\).
03

Define the numbers for which the rational expression is undefined

So, the denominator becomes zero when \(x = 5\). Therefore, the rational expression \(\frac{17}{6x-30}\) is undefined for \(x = 5\).

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Most popular questions from this chapter

Two investments have interest rates that differ by \(1 \% .\) An investment for 1 year at the lower rate earns 175 . The same principal invested for a year at the higher rate earns 200 dollars . What are the two interest rates?

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

Explain how to add rational expressions when denominators are opposites. Use an example to support your explanation.

Explain how to add rational expressions when denominators are the same. Give an example with your explanation.

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