if h(s)=(3s+6)/(s-A);h(2)=-2, solve for A

Given the function \( h(s) = \frac{3s + 6}{s - A} \), and knowing that \( h(2) = -2 \), we need to solve for \( A \).

First, substitute \( s = 2 \) into the function:

\[
h(2) = \frac{3(2) + 6}{2 - A} = -2
\]

Simplify the expression:

\[
\frac{6 + 6}{2 - A} = -2
\]
\[
\frac{12}{2 - A} = -2
\]

Now, solve for \( A \). First, multiply both sides by \( (2 - A) \) to eliminate the denominator:

\[
12 = -2(2 - A)
\]

Expand the right side:

\[
12 = -4 + 2A
\]

Now, solve for \( A \):

\[
12 + 4 = 2A
\]
\[
16 = 2A
\]
\[
A = \frac{16}{2} = 8
\]

Thus, \( A = 8 \).

Would you like further details or explanations?

Here are five related questions:
1. What happens if \( A = 0 \) in the function \( h(s) \)?
2. How would the graph of \( h(s) \) change as \( A \) increases?
3. What is the domain of \( h(s) \) when \( A = 8 \)?
4. Can you find \( s \) if given \( h(s) = 0 \)?
5. What is the horizontal asymptote of \( h(s) \)?

**Tip:** When solving for constants, multiplying to eliminate fractions is an effective first step to simplify the equation.

Explore how to solve the function equation h(s) = (3s + 6) / (s - A) given h(2) = -2. This detailed solution covers function evaluation and solving equations, suitable for students in Grades 9-12.

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