Simplify $\dfrac{4}{aw^2} + \dfrac{16a^3}{5w}$. Answer ...

1. Identify a common denominator and rewrite both fractions over it.

The lowest common denominator of $aw^2$ and $5w$ is $5aw^2$.

$\frac{4}{aw^2}=\frac{20}{5aw^2}$

$\frac{16a^3}{5w}=\frac{16a^3\cdot aw}{5w\cdot aw}=\frac{16a^4w}{5aw^2}$

2. Add the numerators and simplify by factorising the numerator.

$\frac{20}{5aw^2}+\frac{16a^4w}{5aw^2}=\frac{20+16a^4w}{5aw^2}$

Factorise the numerator:

$\frac{20+16a^4w}{5aw^2}=\frac{4(5+4a^4w)}{5aw^2}$