To simplify the expression \(\frac{x^2 - 1}{x + 1} \cdot \frac{x + 5}{5x - 5}\), we will first factor where possible:
- The expression \(x^2 - 1\) can be factored as \((x - 1)(x + 1)\) (difference of squares).
- The expression \(5x - 5\) can be factored as \(5(x - 1)\).
So the expression becomes:
\[ \frac{(x - 1)(x + 1)}{(x + 1)} \cdot \frac{x + 5}{5(x - 1)} \]
Next, we can simplify this:
- The \((x + 1)\) in the numerator and denominator cancels out.
- The \((x - 1)\) in the numerator from the first fraction and the denominator from the second fraction cancels out.
After cancellation, we have:
\[ \frac{x + 5}{5} \]
Thus, the simplified expression is:
\[ \frac{x + 5}{5} \]
Therefore, the correct response is:
x + 5 / 5 (or, in the other notation, Start Fraction x plus 5 over 5 End Fraction).