Final answer:
All values of 'a' are allowed replacements for 'a' in the given expression.
Step-by-step explanation:
The expression is (1)/(2a^(2)+15a+18). We need to find the values of a that are not allowable replacements for 'a' in this expression.
To find the values that are not allowed, we need to consider the denominator of the expression. In this case, the denominator is a quadratic equation of the form ax^2+bx+c. For this equation to be defined, the discriminant (b^2-4ac) must be greater than or equal to zero.
In this case, the discriminant is 15^2-4(2)(18) = 225-144 = 81. Since the discriminant is positive, the quadratic equation has real solutions, which means all values of 'a' are allowed replacements for 'a' in the given expression.