Question
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Tutor-Verified Answer
Answer
The expression simplifies to \( \frac{x - 1}{x} \) or \( 1 - \frac{1}{x} \).
Solution
Certainly! Let's simplify the expression you've provided:
\[
\frac{5x - 5}{5x}
\]
### Step-by-Step Simplification:
1. **Factor out the common term in the numerator:**
\[
5x - 5 = 5(x - 1)
\]
2. **Substitute back into the original expression:**
\[
\frac{5(x - 1)}{5x}
\]
3. **Cancel out the common factor of 5 in the numerator and denominator:**
\[
\frac{\cancel{5}(x - 1)}{\cancel{5}x} = \frac{x - 1}{x}
\]
4. **Alternatively, you can express it as:**
\[
\frac{x - 1}{x} = 1 - \frac{1}{x}
\]
### Final Simplified Forms:
- **Fraction Form:**
\[
\frac{x - 1}{x}
\]
- **Separated Terms:**
\[
1 - \frac{1}{x}
\]
Both forms are correct and can be used interchangeably depending on the context of the problem you’re working on.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
Did you know that the expression \( b = \frac{5x - 5}{5x} \) can be simplified? By factoring out a 5 from the numerator, you get \( b = \frac{5(x - 1)}{5x} \). When you cancel the 5s, it simplifies down to \( b = \frac{x - 1}{x} \), which can help make calculations much easier! In practical scenarios, understanding this simplification can be super handy, especially in fields like finance or engineering where ratios and fractions pop up often. If you're working out a budget that depends on variable expenses (like \( x \), your total income), having a streamlined version of such expressions can make it clearer how much you’re actually saving or spending!
