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To combine the given fractions into one, we will first identify the common denominator.

### Given Expression:

\[
\frac{2}{x + 5} + \frac{3x}{x^2 - 2x - 35}
\]

#### Step 1: Factor the Denominator

Let's factor the quadratic expression in the second fraction:

\[
x^2 - 2x - 35 = (x - 7)(x + 5)
\]

So, the expression now becomes:

\[
\frac{2}{x + 5} + \frac{3x}{(x - 7)(x + 5)}
\]

#### Step 2: Determine the Least Common Denominator (LCD)

The LCD for these fractions is \((x - 7)(x + 5)\).

#### Step 3: Rewrite Each Fraction with the Common Denominator

Rewrite the first fraction with the common denominator:

\[
\frac{2}{x + 5} = \frac{2(x - 7)}{(x - 7)(x + 5)}
\]

Now, we have:

\[
\frac{2(x - 7)}{(x - 7)(x + 5)} + \frac{3x}{(x - 7)(x + 5)}
\]

#### Step 4: Combine the Fractions

Combine the fractions over the common denominator:

\[
\frac{2(x - 7) + 3x}{(x - 7)(x + 5)}
\]

#### Step 5: Simplify the Numerator

Expand and simplify the numerator:

\[
2(x - 7) + 3x = 2x - 14 + 3x = 5x - 14
\]

So, the expression becomes:

\[
\frac{5x - 14}{(x - 7)(x + 5)}
\]

### Final Answer:

\[
\frac{5x - 14}{(x - 7)(x + 5)}
\]

This is the combined fraction in its simplest form.

Would you like further details or have any questions?

Here are some related questions you might find interesting:
1. How do you factor quadratic expressions in general?
2. What are the steps to find a common denominator for multiple fractions?
3. Can you provide another example involving adding rational expressions?
4. How do you handle subtraction between two fractions with different denominators?
5. What are some common mistakes to avoid when simplifying fractions?

**Tip:** Always factor the denominators first to find the least common denominator when adding or subtracting fractions.

Perform the operation and combine to one fraction: (2 / (x + 5)) + (3x / (x^2 - 2x - 35)).

Learn how to combine the fractions (2/(x + 5)) + (3x/(x^2 - 2x - 35)) into a single fraction. This solution covers key algebraic concepts including factoring quadratic expressions and finding the least common denominator. Suitable for students in Grades 9-11.

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