https://file.aiquickdraw.com/mathbot/file/17273078741207jn8dg6z.jpg

The expression in the image is:

\[
\frac{3}{10x^2} + \frac{7}{25x}
\]

To add these two fractions, we need a common denominator. Let's first factor both denominators:

- The first denominator is \(10x^2\).
- The second denominator is \(25x\).

The least common denominator (LCD) between \(10x^2\) and \(25x\) is \(50x^2\).

### Step 1: Rewrite each fraction with the LCD as the denominator.
- The first fraction becomes:
  \[
  \frac{3}{10x^2} = \frac{3 \cdot 5}{10x^2 \cdot 5} = \frac{15}{50x^2}
  \]
- The second fraction becomes:
  \[
  \frac{7}{25x} = \frac{7 \cdot 2x}{25x \cdot 2x} = \frac{14x}{50x^2}
  \]

### Step 2: Add the two fractions:
Now that both fractions have the same denominator, we can add them:
\[
\frac{15}{50x^2} + \frac{14x}{50x^2} = \frac{15 + 14x}{50x^2}
\]

Thus, the result is:

\[
\frac{15 + 14x}{50x^2}
\]

Would you like further details or have any questions? Here are 5 related questions:

1. How do you find the least common denominator between two fractions?
2. How would this problem change if the exponents of \(x\) were different in both denominators?
3. Can you simplify the final expression further?
4. What are the steps to subtract similar algebraic fractions?
5. How can this method be extended to more complex fractions?

**Tip:** When adding fractions, always ensure the denominators are identical before combining the numerators.

This lesson covers how to add algebraic fractions, specifically adding 3/(10x^2) + 7/(25x). Learn how to find the least common denominator and simplify the result, with step-by-step instructions. Ideal for students in Grades 8-10.

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