The value that must be excluded from the domain of the expression (x²-1)/(x) is x=0 because this makes the denominator zero and division by zero is undefined in math. The other values x=3, x=1, and x=-1 are valid as they don't make the denominator zero.
In mathematics, especially in algebra, the domain of a function is the set of input or argument values for which the function is defined. In this case, the function is (x²-1)/(x). For this function to be defined, the denominator, x should not be equal to zero. This is because dividing by zero is undefined in mathematics.
So, the value that must be excluded from the domain of the variable in the expression (x²-1)/(x), is x=0. All other values x=3, x=1, and x=-1 are included in the domain since substituting them in place of x in the expression doesn't make the denominator zero and hence, these values are valid.
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