Answer: THIRD OPTION.
Step-by-step explanation:
We need to remember that we can create a perfect square trinomial by squaring a binomial:
[tex](a\±b)^2=a^2\±2ab+b^2[/tex]
Then we need need to pick the coefficient of the x term of the given expression, divide it by 2 and square it:
[tex](\frac{3}{2})^2=\frac{9}{4}[/tex]
Therefore, the number that should be added to the given expression in order to create a perfect square trinomial is:
[tex]\frac{9}{4}[/tex]
