Question

add.
\\(\frac{w^{3}}{8ad} + \frac{3av}{2c^{3}d^{2}}\\)
simplify your answer as much as possible.

Explanation:

Step1: Find least common denominator

The denominators are $8ad$ and $2c^3d^2$. The least common denominator (LCD) is $8ac^3d^2$.

Step2: Rewrite fractions with LCD

For $\frac{w^3}{8ad}$, multiply numerator and denominator by $c^3d$:
$\frac{w^3 \cdot c^3d}{8ad \cdot c^3d} = \frac{w^3c^3d}{8ac^3d^2}$

For $\frac{3av}{2c^3d^2}$, multiply numerator and denominator by $4a$:
$\frac{3av \cdot 4a}{2c^3d^2 \cdot 4a} = \frac{12a^2v}{8ac^3d^2}$

Step3: Add the fractions

Add the numerators over the common LCD:
$\frac{w^3c^3d + 12a^2v}{8ac^3d^2}$

Answer:

$\frac{w^3c^3d + 12a^2v}{8ac^3d^2}$