Question

Write the polynomial expression in simplest form: x^2−1/x+1 ⋅x+5/5x−5
(1 point)
Responses

x+55
the fraction with numerator x plus 5 and denominator 5

x + 5
x + 5

x
x

x5

Answer 1

To simplify the expression \((\frac{x^2 - 1}{x + 1}) \cdot \frac{x + 5}{5x - 5}\), we can follow these steps:

1. Factor the expressions where applicable:
- \(x^2 - 1\) is a difference of squares: \(x^2 - 1 = (x - 1)(x + 1)\).
- \(5x - 5\) can be factored: \(5(x - 1)\).

2. Rewrite the expression:
\[
\frac{(x - 1)(x + 1)}{(x + 1)} \cdot \frac{x + 5}{5(x - 1)}
\]

3. Simplify the fractions:
- The \((x + 1)\) in the numerator and denominator cancels out.
- The \((x - 1)\) in the numerator and denominator cancels out as well.

Now, we are left with:
\[
\frac{x + 5}{5}
\]

This result in simplest form represents the fraction with numerator \(x + 5\) and denominator \(5\).

Thus, the answer is:
**the fraction with numerator \(x + 5\) and denominator \(5\)**.