Which choice is the appropriate simplified form and restriction for the variable? 3x^2+9x over x^2-2x-15

(3x^2 + 9x) / (x^2 - 2x - 15)

Factor both polynomials

(3x) (x+3) / (x-5) (x+3) = 3x / (x+5)

The simplified form is 3x / (x+5)

The restriction for the variable is x ≠ - 3 (this is because you can only simplify the factor x-3 if its value is not zero).

If you would like to know what is the appropriate simplified form and restriction for the variable, you can calculate this using the following steps:

(3x^2 + 9x) / (x^2 - 2x - 15) = (3x * (x + 3)) / ((x - 5) * (x + 3)) = 3x / (x - 5)

The simplified form is 3x / (x - 5) and the restriction for the variable would be x ≠ 5 and x ≠ - 3.