Question

Write the polynomial expression in simplest form: x2−1x+1×x+55x−5 (1 point) Responses x+1 x+1 x+5 x+5 x x x+55

Answer 1

To simplify the polynomial expression \( \frac{x^2 - 1}{x + 1} \times \frac{x + 5}{5x - 5} \), we start by simplifying each part.

First, simplify \( \frac{x^2 - 1}{x + 1} \):
- Notice that \( x^2 - 1 \) is a difference of squares: \( x^2 - 1 = (x + 1)(x - 1) \).
- So, we have:
\[
\frac{x^2 - 1}{x + 1} = \frac{(x + 1)(x - 1)}{x + 1}
\]
- As long as \( x \neq -1 \), this simplifies to \( x - 1 \).

Next, simplify \( \frac{x + 5}{5x - 5} \):
- Factor out a 5 in the denominator:
\[
5x - 5 = 5(x - 1)
\]
- Thus, we have:
\[
\frac{x + 5}{5(x - 1)}
\]

Now we can combine both parts:
\[
(x - 1) \times \frac{x + 5}{5(x - 1)}.
\]
As long as \( x \neq 1 \) (to avoid division by zero), the \( x - 1 \) terms cancel out:
\[
\frac{x + 5}{5}.
\]

So the expression simplifies to:
\[
\frac{x + 5}{5}.
\]

This can also be written as:
\[
\frac{1}{5}(x + 5).
\]

Therefore, in simplest form, the expression is:
\[
\frac{x + 5}{5}.
\]