Subtract $\frac{x}{8}$ from $\frac{25}{4}$ to get $\frac{-x+50}{8}$.

To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $2$.

Add $\frac{x^2}{2}$ and $\frac{5}{2}$ to get $\frac{x^2+5}{2}$.

To add expressions with the same denominators, we add the numerators and write the result over the common denominator.

Divide $\frac{-x+50}{8}$ by $\frac{x^2+5}{2}$ to get $\frac{-2x+100}{8x^2+40}$.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.