Answer
$\dfrac{10+3x}{2x^2}$
Work Step by Step
RECALL:
$(f+g)(x) = f(x)+g(x)$
Using the formula above gives:
$(r+t)(x)
\\= r(x)+t(x)
\\=\dfrac{5}{x^2}+\dfrac{3}{2x}$
Make the expressions similar using their LCD $2x^2$
$=\dfrac{5(2)}{x^2(2)}+\dfrac{3(x)}{2x(x)}
\\=\dfrac{10}{2x^2}+\dfrac{3x}{2x^2}
\\=\dfrac{10+3x}{2x^2}$