https://file.aiquickdraw.com/mathbot/file/1725509422781tgj1wp65.jpg

Let's evaluate both expressions given that \( h = -2 \).

### 1) First Expression:
\[
8 + \frac{6 + h}{7h} - 10
\]

Substitute \( h = -2 \) into the expression:
\[
8 + \frac{6 + (-2)}{7(-2)} - 10
= 8 + \frac{6 - 2}{-14} - 10
= 8 + \frac{4}{-14} - 10
= 8 - \frac{2}{7} - 10
\]
Simplify:
\[
8 - 10 = -2
\]
So:
\[
-2 - \frac{2}{7} = -2 - 0.2857 \approx -2.2857
\]
Thus, the result of the first expression is approximately:
\[
\boxed{-2.2857}
\]

---

### 2) Second Expression:
\[
\frac{3}{h} + \frac{(10h - 4)^2}{h + 3}
\]

Substitute \( h = -2 \) into the expression:
\[
\frac{3}{-2} + \frac{(10(-2) - 4)^2}{-2 + 3}
= \frac{3}{-2} + \frac{(-20 - 4)^2}{-2 + 3}
= \frac{3}{-2} + \frac{(-24)^2}{1}
= -1.5 + 576
\]
Simplify:
\[
-1.5 + 576 = 574.5
\]
Thus, the result of the second expression is:
\[
\boxed{574.5}
\]

Would you like any further clarification or detailed steps on this?

Here are five related questions for further practice:
1. What happens if \( h \) were equal to zero in the second expression?
2. How would the results change if \( h = 1 \)?
3. Can you simplify the second expression before substituting \( h \)?
4. What is the result of the first expression if \( h = 3 \)?
5. Can the second expression be factored for different values of \( h \)?

**Tip:** Always simplify expressions as much as possible before plugging in values—it can make calculations easier!

Evaluate each expression when h = -2: 1) 8 + (6 + h) / (7h) - 10  2) (3 / h) + ((10h - 4)^2) / (h + 3)

This solution demonstrates how to evaluate algebraic expressions by substituting the value of h = -2. Learn the step-by-step process to solve rational expressions and simplify results. Suitable for students in Grades 9-10.

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