List all numbers that must be excluded from the domain of each rational expression. 3/(2x² + 4x - 9)

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Identify the domain of a rational expression: The domain consists of all real numbers except those that make the denominator equal to zero. For this problem, the denominator is 2x^2 + 4x - 9.

Set the denominator equal to zero to find the values of x that must be excluded: 2x^2 + 4x - 9 = 0.

Simplify the quadratic equation: Divide through by 2 to make the equation simpler, resulting in x^2 + 2x - 4.5 = 0.

Solve the quadratic equation using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a, where a = 1, b = 2, and c = -4.5.

Calculate the discriminant (b^2 - 4ac) and substitute the values into the quadratic formula to find the two solutions for x. These solutions are the values that must be excluded from the domain.

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