We are given the expression:

\[
\frac{3(z - 9)}{z + 5}
\]

and the value of \( z = 6 \).

### Step 1: Substitute \( z = 6 \) into the expression.
\[
\frac{3(6 - 9)}{6 + 5} = \frac{3(-3)}{11}
\]

### Step 2: Simplify.
\[
\frac{3(-3)}{11} = \frac{-9}{11}
\]

Thus, the value of the expression when \( z = 6 \) is:

\[
\frac{-9}{11}
\]

Let me know if you'd like more details or have any questions! Here are some related questions:

1. What if \( z = 0 \)? How would the expression change?
2. How would the result differ if the numerator had been \( 3(z + 9) \)?
3. What happens if \( z = -5 \)? Why is this case special?
4. Can you rewrite this expression to eliminate the denominator for certain values of \( z \)?
5. What if we had a different constant in the denominator, such as \( z - 5 \)?

**Tip:** Always check if the denominator becomes zero for certain values of \( z \), as this makes the expression undefined.

The query submitted by the user: 3(z–9) z=6 – z+5

Learn how to simplify the algebraic expression 3(z - 9) / (z + 5) with the value of z = 6. This step-by-step guide covers substitution in algebraic expressions and fraction simplification, perfect for students in Grades 6-8.

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