To solve the equation \( g = \frac{x - c}{x} \) for \( x \), follow these steps:

### Step 1: Multiply both sides by \( x \)
Multiply both sides of the equation by \( x \) to eliminate the denominator:

\[
g \cdot x = x - c
\]

### Step 2: Rearrange the equation
Move all terms involving \( x \) to one side:

\[
g \cdot x - x = -c
\]

### Step 3: Factor out \( x \)
Factor out \( x \) on the left-hand side:

\[
x(g - 1) = -c
\]

### Step 4: Solve for \( x \)
Now, solve for \( x \) by dividing both sides by \( (g - 1) \):

\[
x = \frac{-c}{g - 1}
\]

Thus, the solution for \( x \) is:

\[
x = \frac{-c}{g - 1}
\]

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Would you like more details or have any questions?

Here are 5 related questions:
1. What happens if \( g = 1 \) in the equation?
2. How does the solution change if \( c = 0 \)?
3. Can you derive the same solution using another method?
4. What are the implications for \( x \) if \( g < 1 \)?
5. Can this equation be applied to any real-world scenarios?

**Tip:** Always check for cases where the denominator becomes zero to avoid undefined values.

Learn how to solve the rational equation g = (x - c) / x for x with a detailed step-by-step solution. This problem covers key algebraic concepts and formulas and is suitable for students in Grades 8-10.

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