Evaluate equation h(x) =3x/x+2 find h(2) 

To evaluate the equation \( h(x) = \frac{3x}{x + 2} \) at \( x = 2 \), follow these steps:

1. Substitute \( x = 2 \) into the equation:
   \[
   h(2) = \frac{3(2)}{2 + 2}
   \]

2. Simplify the expression:
   \[
   h(2) = \frac{6}{4}
   \]

3. Reduce the fraction to its simplest form:
   \[
   h(2) = \frac{3}{2}
   \]

So, \( h(2) = \frac{3}{2} \).

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

Here are some related questions you might find useful:

1. How do you find the domain of the function \( h(x) = \frac{3x}{x + 2} \)?
2. What is the behavior of \( h(x) \) as \( x \) approaches -2?
3. How do you find the horizontal asymptote of \( h(x) = \frac{3x}{x + 2} \)?
4. What is the vertical asymptote of \( h(x) = \frac{3x}{x + 2} \)?
5. How do you graph the function \( h(x) = \frac{3x}{x + 2} \)?
6. Can \( h(x) = \frac{3x}{x + 2} \) ever be zero? If so, for what value of \( x \)?
7. How do you find the inverse function of \( h(x) = \frac{3x}{x + 2} \)?
8. How does \( h(x) \) change as \( x \) becomes very large (positive or negative)?

**Tip:** When simplifying fractions, always check if the numerator and denominator have common factors that can be canceled out to reduce the fraction to its simplest form.

Learn how to evaluate the function h(x) = 3x/(x + 2) at x = 2 step-by-step. This problem involves rational functions and fraction simplification, suitable for students in Grades 9-12.

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