Final answer:
To find the domain of the variable x in the given equation, we set the denominators of the fractions equal to zero and solve for x. The domain of x is all real numbers except -9 and 9.
Step-by-step explanation:
To find the domain of the variable in the equation (1)/(x² - 81) - (7)/(x - 9) = (1)/(x + 9), we need to consider the possible values that x can take. The domain of the variable x is determined by the values that make the denominators of the fractions non-zero. In this case, we have two denominators: x² - 81 and x - 9. To find the domain, we set each denominator equal to zero and solve for x.
Step 1: Set x² - 81 = 0 and solve for x:
x² - 81 = 0
(x + 9)(x - 9) = 0
x = -9 or x = 9
Step 2: Set x - 9 = 0 and solve for x:
x - 9 = 0
x = 9
Therefore, the domain of the variable x is all real numbers except -9 and 9.