To solve the equation \( 42 = \frac{3}{y} + 9 \), let's isolate \( y \).

### Step 1: Subtract 9 from both sides of the equation
\[
42 - 9 = \frac{3}{y}
\]
\[
33 = \frac{3}{y}
\]

### Step 2: Multiply both sides by \( y \) to eliminate the fraction
\[
33y = 3
\]

### Step 3: Divide both sides by 33
\[
y = \frac{3}{33} = \frac{1}{11}
\]

Thus, the solution is \( y = \frac{1}{11} \).

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. How do you solve more complex rational equations?
2. What happens when \( y \) is in multiple terms in the equation?
3. How do you check if a solution is correct by plugging it back into the equation?
4. What if the equation had \( y^2 \) instead of \( y \)?
5. How do you solve a system of equations involving fractions?

**Tip:** Always check your final answer by substituting it back into the original equation.

Learn how to solve the rational equation 42 = 3/y + 9 with a detailed step-by-step guide. This problem explores basic algebraic manipulations, including isolating the variable and working with fractions. Suitable for students in Grades 7-9.

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