Question
Simplify \( \frac{a^{2}-1}{a-1} \) \[ \begin{array}{l}\text { A. }(a-1)(a+1) \\ \text { OB. } a+1 \\ \text { ut of } a \cdot a-1\end{array} \]
Ask by Zimmerman Valdez. in South Africa
Jan 31,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified form of \(\frac{a^{2}-1}{a-1}\) is \(a + 1\).
Solution
To simplify the expression \(\frac{a^{2}-1}{a-1}\), let's follow these steps:
1. **Factor the numerator**:
\[
a^2 - 1 = (a - 1)(a + 1)
\]
This is a difference of squares, which factors into the product of \((a - 1)\) and \((a + 1)\).
2. **Simplify the fraction**:
\[
\frac{(a - 1)(a + 1)}{a - 1}
\]
You can cancel out the \((a - 1)\) term in the numerator and the denominator, assuming \(a \neq 1\):
\[
= a + 1
\]
**Final Simplified Form**:
\[
a + 1
\]
**Answer:** B. \( a + 1 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To simplify \( \frac{a^{2}-1}{a-1} \), we start by recognizing that \( a^{2}-1 \) can be factored as a difference of squares: \[ a^{2}-1 = (a-1)(a+1) \] Now, substitute this factored form back into the expression: \[ \frac{(a-1)(a+1)}{a-1} \] Next, as long as \( a \neq 1 \), we can cancel out \( a-1 \) from the numerator and the denominator: \[ a+1 \] Thus, the simplified result is: \[ \boxed{a+1} \] This matches option B in your list!
