To simplify the expression:

\[
\frac{-6h + 47}{h - 9}
\]

We check whether it can be simplified further by factoring. Since there are no common factors between the numerator and the denominator, this is already in its simplest form.

Thus, the simplified expression is:

\[
\frac{-6h + 47}{h - 9}
\]

### Do you need further details or clarification?

Here are 5 related questions you might explore:
1. How do you simplify rational expressions in general?
2. What happens if \( h = 9 \) in this expression?
3. How would you divide two rational expressions?
4. Can you find the value of this expression for specific values of \( h \)?
5. How do you perform long division on polynomials?

**Tip**: Always check for any possible factoring in the numerator and denominator when simplifying rational expressions!

Learn how to simplify the rational expression (-6h + 47) / (h - 9). This problem explores key algebraic concepts such as rational expressions, factoring, and simplification, suitable for students in Grades 9-11.

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