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.