To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $\left(b-5\right)\left(b+5\right)$ and $b^{2}+56$ is $\left(b-5\right)\left(b+5\right)\left(b^{2}+56\right)$. Multiply $\frac{8}{\left(b-5\right)\left(b+5\right)}$ times $\frac{b^{2}+56}{b^{2}+56}$. Multiply $\frac{4}{b^{2}+56}$ times $\frac{\left(b-5\right)\left(b+5\right)}{\left(b-5\right)\left(b+5\right)}$.
Since $\frac{8\left(b^{2}+56\right)}{\left(b-5\right)\left(b+5\right)\left(b^{2}+56\right)}$ and $\frac{4\left(b-5\right)\left(b+5\right)}{\left(b-5\right)\left(b+5\right)\left(b^{2}+56\right)}$ have the same denominator, subtract them by subtracting their numerators.
