Let f(x)= x-5 and g(x)= x^2-1 be defined as in the previous example. Express the following
functions as the sum, difference, quotient, or product of f and g of r(x)=x-5\2x^2-2

To express the function \( r(x) = \frac{x-5}{2x^2-2} \) as a combination of \( f(x) \) and \( g(x) \), we start by analyzing how \( r(x) \) can be rewritten in terms of \( f(x) = x - 5 \) and \( g(x) = x^2 - 1 \).

### Step 1: Factor the denominator of \( r(x) \)
First, we factor the denominator \( 2x^2 - 2 \):
\[
2x^2 - 2 = 2(x^2 - 1)
\]
Thus, we can rewrite \( r(x) \) as:
\[
r(x) = \frac{x - 5}{2(x^2 - 1)}
\]

### Step 2: Express \( r(x) \) in terms of \( f(x) \) and \( g(x) \)
Since \( g(x) = x^2 - 1 \), we can substitute \( g(x) \) into the expression:
\[
r(x) = \frac{f(x)}{2g(x)}
\]

### Final Answer:
The function \( r(x) = \frac{x-5}{2x^2-2} \) can be expressed as:
\[
r(x) = \frac{f(x)}{2g(x)}
\]
This represents the quotient of \( f(x) \) and \( 2g(x) \).

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### Related Questions:
1. How do you express the sum of \( f(x) \) and \( g(x

Learn how to express the quotient function r(x) = (x - 5) / (2x^2 - 2) as a combination of functions f(x) = x - 5 and g(x) = x^2 - 1. This problem involves factorizing the denominator and expressing the quotient function in terms of given functions. Suitable for high school students.

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