https://file.aiquickdraw.com/mathbot/file/1725399458872659bshbj.jpg

The given problem in the image is an algebraic expression involving fractions. Here's the expression from the image:

\[
\frac{10p + 20}{3p} + \frac{5p - 10}{p}
\]

To solve this, we need to simplify the expression by finding a common denominator and combining the fractions.

### Step-by-step Solution:

1. **Identify the Denominators:**
   - The denominators in the expression are \(3p\) and \(p\).

2. **Find the Least Common Denominator (LCD):**
   - The LCD for \(3p\) and \(p\) is \(3p\).

3. **Rewrite Each Fraction with the LCD:**
   - The first fraction \(\frac{10p + 20}{3p}\) already has the denominator \(3p\).
   - The second fraction \(\frac{5p - 10}{p}\) needs to be rewritten with a denominator of \(3p\). Multiply both the numerator and denominator by 3:
   
   \[
   \frac{5p - 10}{p} = \frac{3(5p - 10)}{3p} = \frac{15p - 30}{3p}
   \]

4. **Combine the Fractions:**
   - Now that both fractions have the same denominator, combine them:

   \[
   \frac{10p + 20}{3p} + \frac{15p - 30}{3p} = \frac{(10p + 20) + (15p - 30)}{3p}
   \]

5. **Simplify the Numerator:**
   - Combine like terms in the numerator:

   \[
   (10p + 15p) + (20 - 30) = 25p - 10
   \]

   - The expression becomes:

   \[
   \frac{25p - 10}{3p}
   \]

6. **Factor the Numerator (if possible):**
   - The numerator \(25p - 10\) can be factored as:

   \[
   25p - 10 = 5(5p - 2)
   \]

   - So, the simplified expression is:

   \[
   \frac{5(5p - 2)}{3p}
   \]

7. **Final Simplified Expression:**

   \[
   \frac{5(5p - 2)}{3p}
   \]

This is the simplified form of the given expression.

Would you like more details, or do you have any questions?

### Related Questions:

1. How do you find the least common denominator (LCD) for algebraic fractions?
2. What are some common mistakes to avoid when combining fractions?
3. How can we further simplify a fraction if both the numerator and denominator share a common factor?
4. How do you handle algebraic fractions where the denominators are more complex expressions?
5. What strategies are useful for simplifying fractions involving multiple variables?

### Tip:
Always look for common factors when simplifying fractions, as this can often help to further reduce the expression.

Learn how to simplify algebraic fractions with a detailed step-by-step solution. This problem involves finding a common denominator, combining fractions, and simplifying the expression. Suitable for students in Grades 8-10.

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