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.