Question

Add the rational expressions to find the sum: −4x−4+x2−2x2x−8 . Put the answer into its simplest form.(1 point)
Responses

x2−2x−82x−8
Start Fraction x squared minus 2 x minus 8 over 2 x minus 8 End Fraction

x2−2x2x
Start Fraction x squared minus 2 x over 2 x End Fraction

x2−2x−4x−4
Start Fraction x squared minus 2 x minus 4 over x minus 4 End Fraction

x+22

Answer 1

Subtract the rational expressions x22x−12−18x−6 . Simplify the answer.(1 point)
Responses

x2−362(x−6)
Start Fraction x squared minus 36 over 2 left parenthesis x minus 6 right parenthesis End Fraction

x2−18x−6
Start Fraction x squared minus 18 over x minus 6 End Fraction

x+62
Start Fraction x plus 6 over 2 End Fraction

x−62

Answer 2

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

x2+2xx2+7x−8−xx−1

(1 point)
Responses

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

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

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

(x−1)(x2+7x−8)

Answer 3

To combine the given rational expressions, we first need to express them with a common denominator. Let's work through this step-by-step.

We are given the following expressions:

\[
-\frac{4}{x-4} + \frac{x^2 - 2}{2x - 8}
\]

Notice that \(2x - 8\) can be factored as \(2(x - 4)\). So we will rewrite the second expression:

\[
-\frac{4}{x-4} + \frac{x^2 - 2}{2(x - 4)}
\]

Now, we can find a common denominator, which will be \(2(x - 4)\).

We rewrite the first expression:

\[
-\frac{4}{x-4} = -\frac{4 \cdot 2}{(x-4) \cdot 2} = -\frac{8}{2(x-4)}
\]

Now we can combine both fractions:

\[
-\frac{8}{2(x - 4)} + \frac{x^2 - 2}{2(x - 4)} = \frac{-8 + (x^2 - 2)}{2(x - 4)}
\]

Now, simplify the numerator:

\[
-8 + x^2 - 2 = x^2 - 10
\]

Thus, we have:

\[
\frac{x^2 - 10}{2(x - 4)}
\]

At this point, we cannot simplify \(x^2 - 10\) further, so the final simplified expression is:

\[
\frac{x^2 - 10}{2(x - 4)}
\]

Among your provided answer choices, this corresponds to none exactly. The closest choice with a similar numerator would be:

\[
\frac{x^2 - 2x - 8}{2x - 8}
\]

However, since our final expression is already simplified, the correct answer for the sum of these rational expressions in simplest form is:

\[
\frac{x^2 - 10}{2(x - 4)}
\]