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To perform the operation and combine the expression into one fraction, we are given:

\[
7 + \frac{5}{x - 9}
\]

First, express \(7\) as a fraction with the same denominator as \(\frac{5}{x - 9}\):

\[
7 = \frac{7(x - 9)}{x - 9} = \frac{7x - 63}{x - 9}
\]

Now, add the two fractions:

\[
\frac{7x - 63}{x - 9} + \frac{5}{x - 9}
\]

Since both fractions have the same denominator, we can combine the numerators:

\[
\frac{7x - 63 + 5}{x - 9} = \frac{7x - 58}{x - 9}
\]

Thus, the final result is:

\[
\frac{7x - 58}{x - 9}
\]

Would you like a deeper explanation or clarification on any step?

Here are 5 related questions:
1. How do you add two fractions with different denominators?
2. What are the steps to simplify an expression like \( \frac{7x - 63}{x - 9} \)?
3. What would happen if the given fraction were subtraction instead of addition?
4. How do you factor a polynomial in the numerator?
5. What is the general strategy for combining fractions with variables?

**Tip:** Always make sure both fractions have the same denominator before adding or subtracting them.

Perform the operation and combine to one fraction: 7 + (5 / (x - 9))

Learn how to perform the operation and combine the expression 7 + 5/(x - 9) into a single fraction. This solution explains the addition of fractions with variables and covers key algebraic concepts. Suitable for students in Grades 9-11.

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