Question

What is the LCD in its factored form of the following rational expression subtraction?

x2+2xx2+7x−8−xx−1

(1 point)
Responses

x(x+2)
x left parenthesis x plus 2 right parenthesis

(x−1)2(x+8)
left parenthesis x minus 1 right parenthesis squared left parenthesis x plus 8 right parenthesis

(x−1)(x+8)
left parenthesis x minus 1 right parenthesis left parenthesis x plus 8 right parenthesis

(x−1)(x2+7x−8)

Answer 1

To find the least common denominator (LCD) in its factored form of the given rational expression subtraction:

\[
\frac{x^2 + 2x}{x^2 + 7x - 8} - \frac{x}{x - 1}
\]

we will first factor each denominator.

1. **Factor the first denominator** \(x^2 + 7x - 8\):
We need to find two numbers that multiply to \(-8\) and add to \(7\). These numbers are \(8\) and \(-1\). Therefore:

\[
x^2 + 7x - 8 = (x + 8)(x - 1)
\]

2. **Factor the second denominator** \(x - 1\):
This is already factored.

Now that we have the denominators factored, the denominators are:
- The first denominator: \((x + 8)(x - 1)\)
- The second denominator: \((x - 1)\)

To determine the least common denominator (LCD), we take the highest power of each factor present in the denominators:

- From \((x + 8)\), we take \(x + 8\).
- From \((x - 1)\), we take \((x - 1)\) (since it appears in both).

Thus, the LCD is:

\[
\text{LCD} = (x + 8)(x - 1)
\]

Therefore, the correct response, expressed in its factored form, is:

\[
(x - 1)(x + 8)
\]

So the answer is:
**(x−1)(x+8)**.