We are given the equation:

\[
\frac{8}{3r} - \frac{9}{4r} = \frac{5}{12}
\]

### Step 1: Find a common denominator on the left-hand side
The denominators are \( 3r \) and \( 4r \). The least common denominator (LCD) of \( 3r \) and \( 4r \) is \( 12r \). So, we rewrite both fractions with \( 12r \) as the denominator:

\[
\frac{8}{3r} = \frac{8 \times 4}{3r \times 4} = \frac{32}{12r}
\]
\[
\frac{9}{4r} = \frac{9 \times 3}{4r \times 3} = \frac{27}{12r}
\]

Now, substitute these into the equation:

\[
\frac{32}{12r} - \frac{27}{12r} = \frac{5}{12}
\]

### Step 2: Combine the fractions on the left-hand side
\[
\frac{32 - 27}{12r} = \frac{5}{12}
\]
\[
\frac{5}{12r} = \frac{5}{12}
\]

### Step 3: Solve for \( r \)
Now, cross-multiply to eliminate the denominators:

\[
5 \times 12 = 5 \times 12r
\]
\[
60 = 60r
\]

### Step 4: Isolate \( r \)
Divide both sides by 60:

\[
r = \frac{60}{60} = 1
\]

Thus, the solution is \( r = 1 \).

Would you like more details, or do you have any questions?

Here are five related questions for practice:
1. Solve \( \frac{5}{2x} - \frac{3}{5x} = \frac{7}{10} \).
2. Solve \( \frac{6}{x} + \frac{2}{3x} = 4 \).
3. Solve \( \frac{4}{5y} - \frac{2}{7y} = \frac{3}{10} \).
4. Solve \( \frac{7}{3z} + \frac{5}{2z} = \frac{11}{6} \).
5. Solve \( \frac{9}{x} - \frac{4}{2x} = \frac{7}{5} \).

**Tip:** Always start by finding a common denominator for rational equations, making the process of combining terms easier.

Learn how to solve the rational equation 8/3r - 9/4r = 5/12 by finding a common denominator and using cross multiplication. This step-by-step solution is suitable for students in Grades 7-9 and covers key algebraic techniques in solving rational equations.

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