Question

For the following equation, a. Write the restrictions on the variable. b. (3)/(x+8)-(4)/(x-8)=(3x)/(x^(2)-64)

Answer 1

The restrictions on the variable in the given equation are x ≠ 8, x ≠ -8, x ≠ 0, x ≠ 4, and x ≠ -4.

Step-by-step explanation:

The restrictions on the variable in the given equation are as follows:

• The variable x cannot equal 8 or -8, as these values would result in division by zero.
• The variable x cannot equal 0, as this would result in division by zero in the term (3x)/(x^2 - 64).
• The variable x cannot equal 4 or -4, as these values would make the equation undefined on the left side.

To summarize, the restrictions on the variable x are x ≠ 8, x ≠ -8, x ≠ 0, x ≠ 4, and x ≠ -4.