Question
\( \leftarrow \begin{array}{l}\frac{1}{x}+8 \\ \frac{1}{x}-6 \\ \text { Simplify. } \\ \text { The simplified expression is } 0 \text { of } 1 \\ \text { (Simplify your answer.) }\end{array} \)
Ask by Carroll Conner. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expressions are \( \frac{1+8x}{x} \) and \( \frac{1-6x}{x} \).
Solution
To simplify the given expressions, we need to combine the terms in each expression.
Given expressions:
1. \( \frac{1}{x} + 8 \)
2. \( \frac{1}{x} - 6 \)
Simplifying each expression:
1. \( \frac{1}{x} + 8 \) simplifies to \( \frac{1+8x}{x} \)
2. \( \frac{1}{x} - 6 \) simplifies to \( \frac{1-6x}{x} \)
Therefore, the simplified expressions are:
1. \( \frac{1+8x}{x} \)
2. \( \frac{1-6x}{x} \)
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To simplify the expression \( \frac{1}{x}+8 + \frac{1}{x}-6 \), first combine like terms. This gives us \( 2 \cdot \frac{1}{x} + (8 - 6) \), which simplifies to \( 2 \cdot \frac{1}{x} + 2 \). Next, to combine these, we can rewrite 2 as \( \frac{2x}{x} \), yielding \( \frac{2}{x} + \frac{2x}{x} = \frac{2 + 2x}{x} \). Thus, the simplified expression becomes \( \frac{2(x + 1)}{x} \). Now, if the expression simplifies further, for it to be zero, the numerator must be zero. Therefore, \( 2(x + 1) = 0 \) leads to \( x + 1 = 0 \) or \( x = -1 \). Hence, the simplified expression is \(\frac{2(x + 1)}{x}\), where \( x \neq 0 \).
