Solve for \( u \) \[ \frac{u}{2}-\frac{5}{6}=\frac{u}{3} \]

To solve the equation for \( u \): \[ \frac{u}{2} - \frac{5}{6} = \frac{u}{3} \] **Step 1: eliminate the fractions** Find the least common multiple (LCM) of the denominators \( 2 \), \( 3 \), and \( 6 \), which is \( 6 \). Multiply every term in the equation by \( 6 \) to eliminate the denominators: \[ 6 \cdot \frac{u}{2} - 6 \cdot \frac{5}{6} = 6 \cdot \frac{u}{3} \] **Step 2: simplify each term** \[ 3u - 5 = 2u \] **Step 3: isolate \( u \)** Subtract \( 2u \) from both sides to get all \( u \) terms on one side: \[ 3u - 2u - 5 = 0 \] \[ u - 5 = 0 \] **Step 4: solve for \( u \)** Add \( 5 \) to both sides: \[ u = 5 \] **Solution:** \[ u = 5 \]