https://file.aiquickdraw.com/mathbot/file/17270909387955l47qdjs.jpg

The expression in the image is:

\[
\frac{2a^2 + 36bc^3}{2ab^2c}
\]

Let's simplify this step by step:

### Step 1: Factor the numerator
The numerator is \( 2a^2 + 36bc^3 \). We can factor out a 2:

\[
2(a^2 + 18bc^3)
\]

### Step 2: Write the expression with the factored numerator
Now the expression becomes:

\[
\frac{2(a^2 + 18bc^3)}{2ab^2c}
\]

### Step 3: Cancel the common factor of 2
The factor of 2 cancels out from both the numerator and the denominator:

\[
\frac{a^2 + 18bc^3}{ab^2c}
\]

### Step 4: Simplify the fraction
Now we simplify each term:
- The term \( \frac{a^2}{ab^2c} = \frac{a}{b^2c} \)
- The term \( \frac{18bc^3}{ab^2c} = \frac{18c^2}{b} \)

### Final Result:
So, the simplified expression is:

\[
\frac{a}{b^2c} + \frac{18c^2}{b}
\]

Would you like any further explanation or details?

Here are some related questions for further practice:
1. How can we simplify rational expressions further?
2. What are the steps to factor polynomials?
3. How do we handle different exponents in rational expressions?
4. Can you explain how to identify common factors in algebraic expressions?
5. How would this process change if the exponents were negative?

**Tip:** Always check if you can factor or cancel terms before simplifying expressions. This can make the process much easier!

Simplify the expression: (2a^2 + 36bc^3) / (2ab^2c)

This page provides a step-by-step solution for simplifying the algebraic expression (2a^2 + 36bc^3) / (2ab^2c). Key algebraic concepts include factoring, properties of exponents, and rational expressions. Suitable for students in Grades 8-10.

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