Find the Domain ((c+5)(c-5))/((c-5)(c+2))

Problem

((c+5)*(c−5))/((c−5)*(c+2))

Solution

1. Identify the denominator of the rational expression, as the domain of a rational function includes all real numbers except those that make the denominator equal to zero.

2. Set the denominator equal to zero to find the excluded values:

(c−5)*(c+2)=0

3. Apply the zero product property to solve for c

c−5=0⇒c=5

c+2=0⇒c=−2

4. State the domain by excluding these values from the set of all real numbers. Even though the factor (c−5) appears in the numerator, the value c=5 still causes division by zero in the original expression and must be excluded.

Final Answer

Domain: *{[c∈ℝ,c≠5,c≠−2]}

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