Find the Domain (v-5)/(v^2-1)+(5-v)/(1-v^2)

Problem

(v−5)/(v2−1)+(5−v)/(1−v2)

Solution

1. Identify the condition for the domain of a rational expression, which requires that the denominators cannot be equal to zero.

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

v2−1=0

3. Factor the difference of squares:

(v−1)*(v+1)=0

4. Solve for v to find the first set of restricted values:

v=1,v=−1

5. Set the second denominator equal to zero:

1−v2=0

6. Factor the second expression:

(1−v)*(1+v)=0

7. Solve for v to find the second set of restricted values:

v=1,v=−1

8. Combine the restrictions to state that v can be any real number except 1 and −1

Final Answer

Domain: *{[v∈ℝ,v≠1,v≠−1]}

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