The error is that in a subtraction the fractions, you don't subtract the numerators and denominators. We have to apply the least common multiple. S
The correct solution is:
[tex]\frac{3}{4}-\frac{9}{2}=\frac{3}{4}-\frac{18}{4}=\frac{3-18}{4}=-\frac{15}{4}[/tex]