Decompose the Expression: Factoring (ab/cd²) + (a²b/c²d) + (ab²/cd³)

Decompose the following expression into factors:

$\frac{ab}{cd^2}+\frac{a^2b}{c^2d}+\frac{ab^2}{cd^3}$

To solve this problem, we'll follow these steps:

• Step 1: Identify the greatest common factor (GCF) of the numerators.
• Step 2: Factor out the GCF from the original expression.
• Step 3: Simplify the resulting expression inside the parentheses.

Now, let's work through each step:
Step 1: The numerators of the terms are $ab$, $a^2b$, and $ab^2$. The GCF here is $ab$.

Step 2: Factor $ab$ from the expression:

Step 3: Factor $\frac{1}{cd}$ from the expression inside the parenthesis to simplify further:

Therefore, the solution to the problem is $\frac{ab}{cd}(\frac{1}{d}+\frac{a}{c}+\frac{b}{d^2})$.