Question

only use the responses i gave you

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

x−62
Start Fraction x minus 6 over 2 End Fraction

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

x2−18x−6

Answer 1

To subtract the rational expressions \( \frac{x^2}{2x - 12} - \frac{18}{x - 6} \), we first need a common denominator.

1. The first fraction can be rewritten as \( \frac{x^2}{2(x - 6)} \).
2. The second fraction can be rewritten as \( \frac{18}{x - 6} \) (we need to express this with the common denominator as well).

Now we can rewrite the second fraction:

\[
\frac{18}{x - 6} = \frac{18 \cdot 2}{2(x - 6)} = \frac{36}{2(x - 6)}
\]

Now we can perform the subtraction:

\[
\frac{x^2}{2(x - 6)} - \frac{36}{2(x - 6)} = \frac{x^2 - 36}{2(x - 6)}
\]

We can simplify \( x^2 - 36 \) as it can be factored:

\[
x^2 - 36 = (x - 6)(x + 6)
\]

Thus, we have:

\[
\frac{(x - 6)(x + 6)}{2(x - 6)}
\]

Since \( x - 6 \) in the numerator and denominator can be canceled (as long as \( x \neq 6 \)), we get:

\[
\frac{x + 6}{2}
\]

Thus, the simplified answer is:

\[
\frac{x + 6}{2}
\]

From your responses, the correct option is:

\[
\text{Start Fraction x plus 6 over 2 End Fraction}
\]