Problem 4
Question
Find all numbers that must be excluded from the domain of each rational expression. $$\frac{x+7}{x^{2}-49}$$
Step-by-Step Solution
Verified Answer
The values x = -7 and x = 7 are to be excluded from the domain of the given rational expression.
1Step 1: Identify the denominator and set it equals to zero
We have \(x^{2}-49 = 0\). This is a standard quadratic equation that can be factored into (x-7)(x+7) = 0.
2Step 2: Solve the equation for x
Setting each factor equal to zero gives x-7 = 0 or x + 7 = 0. So the solutions are x = 7 and x = -7.
3Step 3: Exclude these values from the domain
The domain of a rational function excludes values that make the denominator equal to zero. Therefore, the values x = -7 and x = 7 need to be excluded from the domain of the given rational expression.
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