What must be added to this expression
to make it a perfect square?

9/16 must be added to this expression [tex]x^{2} -3x/2[/tex] to make it a perfect square.According to the question,We have the following expression:[tex]x^{2}[/tex] -3x/2Now, in the given four options, we only have two perfect squares which 9/16 and 16/9.Now, 9/16 is the square of 3/4.So, we will first solve it using 9/16:[tex]x^{2}[/tex]-3x/2+9/16Now, this formula is of identity [tex](a-b)^{2}[/tex] where we have a = x and b = 3/4.The formula of the identity [tex](a-b)^{2} = a^{2} + b^{2} -2ab[/tex].Now, adding 9/16 make it a perfect whole square.(More to know: we can add or subtract a number or a term from an expression to make it a perfect square or perfect cube.)Hence, the correct option is C.To know more about perfect square herehttps://brainly.com/question/385286#SPJ1