Let's solve the equation:

\[
\frac{7}{x} + 9 = \frac{21}{36}
\]

### Step 1: Simplify the fraction on the right-hand side
\[
\frac{21}{36} = \frac{7}{12}
\]

So the equation becomes:
\[
\frac{7}{x} + 9 = \frac{7}{12}
\]

### Step 2: Subtract 9 from both sides
\[
\frac{7}{x} = \frac{7}{12} - 9
\]

First, express 9 with the denominator of 12:
\[
9 = \frac{108}{12}
\]

Now subtract:
\[
\frac{7}{x} = \frac{7}{12} - \frac{108}{12} = \frac{-101}{12}
\]

### Step 3: Solve for \( x \)
Multiply both sides by \( x \) and then by 12:
\[
7 = \frac{-101}{12} \cdot x
\]

Multiply both sides by 12:
\[
84 = -101x
\]

Now, divide both sides by -101:
\[
x = \frac{84}{-101} = -\frac{84}{101}
\]

### Final answer:
\[
x = -\frac{84}{101}
\]

Would you like more details on any of these steps?

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Here are 5 related questions for further practice:
1. Solve \( \frac{5}{x} + 3 = \frac{10}{15} \).
2. What is the solution to \( \frac{9}{x} + 4 = \frac{3}{7} \)?
3. Solve \( \frac{6}{y} + 7 = \frac{5}{8} \).
4. How do you solve \( \frac{12}{z} + 2 = \frac{1}{4} \)?
5. Solve \( \frac{11}{t} + 5 = \frac{8}{9} \).

**Tip:** Always simplify fractions first to make equations easier to solve.

Learn how to solve the rational equation 7/x + 9 = 21/36 step-by-step. This solution covers algebraic concepts like simplifying fractions and solving equations with rational expressions. Suitable for students in Grades 8-10.

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