Question

Write the polynomial expression in simplest form: x2−1/x+1⋅x+5/5x−5
.(1 point)
Responses

x+5
x plus 5

x5
Start Fraction x over 5 End Fraction

x+55
Start Fraction x plus 5 over 5 End Fraction

x

Answer 1

To simplify the expression \(\frac{x^2 - 1}{x + 1} \cdot \frac{x + 5}{5x - 5}\), we will first factor where possible:

1. The expression \(x^2 - 1\) can be factored as \((x - 1)(x + 1)\) (difference of squares).
2. 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).