Final answer:
The domain of the expression (2x² + 2x) / (7x + 7) is all real numbers except for x = -1, because the denominator cannot be zero. The domain in interval notation is (-∞, -1) ∪ (-1, ∞).
Step-by-step explanation:
To find the domain of the expression (2x² + 2x) / (7x + 7), we need to determine the values of x for which the expression is defined. The only restriction in the domain comes from the denominator, as it cannot equal zero because division by zero is undefined. To find when the denominator is zero, we set 7x + 7 equal to zero and solve for x.
7x + 7 = 0
7x = -7
x = -1
Therefore, the expression is undefined when x = -1. Since this is the only restriction, the domain of the expression is all real numbers except for x = -1. In interval notation, the domain is (-∞, -1) ∪ (-1, ∞).