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To make \( h \) the subject of the equation \( w = \frac{h}{h - a} \), we can proceed with the following steps:

1. Start with the given equation:
   \[
   w = \frac{h}{h - a}
   \]

2. Multiply both sides of the equation by \( h - a \) to eliminate the fraction:
   \[
   w(h - a) = h
   \]

3. Distribute \( w \) on the left side:
   \[
   wh - wa = h
   \]

4. Move all terms involving \( h \) to one side of the equation:
   \[
   wh - h = wa
   \]

5. Factor out \( h \) from the left side:
   \[
   h(w - 1) = wa
   \]

6. Finally, solve for \( h \) by dividing both sides by \( w - 1 \):
   \[
   h = \frac{wa}{w - 1}
   \]

So, the subject \( h \) is given by:
\[
h = \frac{wa}{w - 1}
\]

Would you like any further details or have any questions?

Here are five questions that build on this topic:

1. How would you solve for \( a \) if \( h \) and \( w \) were given?
2. What happens to \( h \) if \( w \) approaches 1?
3. How can you check if your answer for \( h \) is correct?
4. What kind of function is represented by \( w = \frac{h}{h - a} \) when graphed in terms of \( h \)?
5. How would the process change if the equation was \( w = \frac{h + b}{h - a} \)?

**Tip:** When solving for a variable, always ensure you properly isolate the variable and check for any potential restrictions on the domain of the function.

This page provides a step-by-step solution to making h the subject of the equation w = h / (h - a). Key algebraic concepts include rearranging formulas and basic algebraic manipulation. Suitable for students in Grades 9-11.

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