Find the Domain 1/(x+5)+10/(x^2-25)=1

Problem

1/(x+5)+10/(x2−25)=1

Solution

1. Identify the denominators in the equation that contain the variable x

2. Factor the quadratic denominator x2−25 using the difference of squares formula.

x2−25=(x+5)*(x−5)

3. Set each unique factor in the denominators to be not equal to zero, as division by zero is undefined.

x+5≠0

x−5≠0

4. Solve the inequalities for x to find the values that must be excluded from the domain.

x≠−5

x≠5

5. Express the domain in interval notation by excluding these two values from the set of all real numbers.

Final Answer

Domain:(−∞,−5)∪(−5,5)∪(5,∞)

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