Solve for $$ u $$ $$ \frac{u}{2}-\frac{5}{6}=\frac{u}{3} $$

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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:**

$$
u = 5
$$
$$ u = 5 $$

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