Multiply each term of $\left(21x^2+10x+8\right)$ by each term in $\left(21x^2+10x+8\right)$.

Combine like terms:

Multiply each term of $\left(441x^4+420x^3+436x^2+160x+64\right)$ by each term in $\left(21x^2+10x+8\right)$.

Combine like terms:

Subtract $\frac{84x+60}{21x^2+10x+8}$ from $\frac{42x+10}{9261x^6+13230x^5+16884x^4+11080x^3+6432x^2+1920x+512}$ to get $\frac{-37044x^5-61740x^4-61824x^3-39600x^2-14934x-3830}{9261x^6+13230x^5+16884x^4+11080x^3+6432x^2+1920x+512}$.

To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $441x^4+420x^3+436x^2+160x+64$.