https://file.aiquickdraw.com/mathbot/file/172638444120405cvplnz.jpg

The expression provided in the image is:

\[
\frac{x - 4}{4x - 16}
\]

### Simplification:

We can factor the denominator to simplify the expression. Notice that \( 4x - 16 \) has a common factor of 4:

\[
4x - 16 = 4(x - 4)
\]

Now, the expression becomes:

\[
\frac{x - 4}{4(x - 4)}
\]

Next, we can cancel the common factor \( x - 4 \) from both the numerator and denominator, assuming \( x \neq 4 \) (because division by zero is undefined):

\[
\frac{1}{4}
\]

Thus, the simplified expression is:

\[
\frac{1}{4}
\]

### Final Answer:
\[
\frac{x - 4}{4x - 16} = \frac{1}{4}, \text{ provided } x \neq 4.
\]

Would you like more details on this simplification or have any questions?

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Here are 5 related questions for further exploration:
1. What is the importance of factoring in algebraic expressions?
2. How do you handle expressions where division by zero might occur?
3. What are some common strategies for simplifying algebraic fractions?
4. How can you determine if two expressions are equivalent?
5. Why is it necessary to state restrictions on variable values, such as \(x \neq 4\)?

**Tip:** Always look for common factors in the numerator and denominator of a fraction before attempting more complex operations.

Simplify the algebraic expression: (x - 4) / (4x - 16)

Learn how to simplify the rational expression (x - 4) / (4x - 16) by factoring and reducing common terms. This algebraic problem introduces factoring techniques and discusses restrictions on variable values to avoid division by zero. Suitable for students in Grades 8-10.

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