Final answer:
The excluded value of the expression (x+5)/((x-2)(x+5)) is x = 2, because at this value the denominator becomes zero, making the expression undefined.
Step-by-step explanation:
Excluded Values of Rational Expressions
To find the excluded values of the rational expression (x+5)/((x-2)(x+5)), we need to determine the values of x that would make the denominator equal to zero. Since division by zero is undefined, any value of x that accomplishes this is considered an excluded value. In this expression, there are two factors in the denominator: x-2 and x+5. Setting each factor equal to zero gives us the equations x - 2 = 0 and x + 5 = 0. Solving these equations, we find that the excluded values of x are 2 from the first equation and -5 from the second equation.
The excluded values of the expression are x = -5 and x = 2. These values make the denominator zero, which results in division by zero. Division by zero is undefined in mathematics. Therefore, these values must be excluded from the domain of the expression.
However, since x + 5 is also a factor in the numerator, it cancels out, leaving x = -5 as a non-excluded value. Therefore, the only true excluded value for this expression is x = 2.
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