To identify a removable discontinuity of a function, we examine the function's factored form and determine where a discontinuity can be removed (typically when a factor cancels out).

General Steps:

1. Identify the function: If given explicitly, factorize the numerator and denominator.
2. Find common factors: Look for terms in the numerator and denominator that cancel each other.
3. Determine the removable discontinuity: The value of $x$ where cancellation occurs is the removable discontinuity.

If you can provide the specific function, I can solve it explicitly. Based on the options provided ($x = -5, -2, 2, 5$), one of these is likely where the numerator and denominator share a common factor.

Could you provide the full function or confirm if factoring has already been done? This will allow me to pinpoint the discontinuity clearly.

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Would you like a detailed breakdown of the process?

Related Questions:

1. What is a removable discontinuity, and how is it defined?
2. How does a removable discontinuity differ from a non-removable one?
3. Can a function have more than one removable discontinuity?
4. What happens to the graph of a function at a removable discontinuity?
5. Why is factoring important in identifying removable discontinuities?

Tip:

Always check for cancellation of terms in the numerator and denominator to identify removable discontinuities.