Is the answer a>2 and a<-2?(2x+3)/x is NOT 3. 2x/x is NOT 0, and even if it was 0, you still need to divide the 3 by x!
(2x+3)/x = (2x/x) + (3/x) = 2 + 3/x.
Think about what is required for the line y=ax (a line that crosses the origin) to cross the function in exactly one place. Do not use algebra, but rather think how this can be done. Draw lines and figure out the requirement for the slope.