To express the function $r(x) = \frac{x - 5}{2x^2 - 2}$ in terms of $f(x)$ and $g(x)$, where $f(x) = x - 5$ and $g(x) = x^2 - 1$, follow these steps:

1. Simplify the denominator of $r(x)$:

   Notice that the denominator $2x^2 - 2$ can be factored as: $2x^2 - 2 = 2(x^2 - 1)$

2. Rewrite $r(x)$ using the factored denominator:

   Substitute this into $r(x)$: $r(x) = \frac{x - 5}{2(x^2 - 1)}$

3. Express $r(x)$ in terms of $f(x)$ and $g(x)$:

   Now substitute $f(x) = x - 5$ and $g(x) = x^2 - 1$: $r(x) = \frac{f(x)}{2g(x)}$

So, the function $r(x)$ can be expressed as: $r(x) = \frac{f(x)}{2g(x)}$

This means that $r(x)$ is the quotient of $f(x)$ and $2g(x)$.

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Would you like further details or have any questions?

Here are some related questions for practice:

1. What is the sum of $f(x)$ and $g(x)$?
2. What is the product of $f(x)$ and $g(x)$?
3. How would you express $r(x) = \frac{x - 3}{x^2 + 1}$ using different functions?
4. Can you find the difference $f(x) - g(x)$?
5. How would the function $h(x) = 3f(x) + 4g(x)$ be expressed?

Tip: When working with functions, always check if the expressions can be simplified or factored before substituting in known functions. This can make the process easier and more straightforward.