To solve the equation \( y = \frac{2 - x}{3 + x} \) for \( x \), follow these steps:

### Step 1: Cross-multiply
Multiply both sides by \( 3 + x \) to eliminate the fraction:

\[
y(3 + x) = 2 - x
\]

### Step 2: Distribute \( y \) on the left side
\[
3y + xy = 2 - x
\]

### Step 3: Get all terms involving \( x \) on one side and the constant terms on the other side
\[
xy + x = 2 - 3y
\]

### Step 4: Factor out \( x \) on the left side
\[
x(y + 1) = 2 - 3y
\]

### Step 5: Solve for \( x \)
Divide both sides by \( y + 1 \):

\[
x = \frac{2 - 3y}{y + 1}
\]

So, the solution is:

\[
x = \frac{2 - 3y}{y + 1}
\]

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. How would the solution change if the equation were \( y = \frac{2 + x}{3 - x} \)?
2. What is the domain of the function \( y = \frac{2 - x}{3 + x} \)?
3. How can you graph the function \( y = \frac{2 - x}{3 + x} \)?
4. What happens to \( x \) as \( y \) approaches infinity in the equation \( y = \frac{2 - x}{3 + x} \)?
5. What is the inverse of the function \( y = \frac{2 - x}{3 + x} \)?

**Tip:** When solving for a variable, it is helpful to isolate the terms with the variable on one side of the equation to simplify the solution process.

Discover how to solve the rational equation y = (2 - x) / (3 + x) for x with a clear, step-by-step explanation. This problem involves core algebraic concepts such as cross-multiplication and properties of equality, suitable for students in Grades 8-10.

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