Question: Solve for \( u \). \[ - \frac{3}{u - 3} = 8 \] Simplify your answer as much as possible…

Solve for \( u \).

\[

• \frac{3}{u - 3} = 8 \]

Simplify your answer as much as possible.

\( u = \boxed{\phantom{0}} \)

Solution

To solve the equation \[ -\frac{3}{u-3} = 8 \] we follow these steps: First, multiply both sides by \(u-3\) to eliminate the fraction: \[ -3 = 8(u-3) \] Next, distribute the 8 on the right side: \[ -3 = 8u - 24 \] Add 24 to both sides to isolate the term with \(u\): \[ 21 = 8u \] Finally, divide both sides by 8 to solve for \(u\): \[ u = \frac{21}{8} \] The solution is \(u = \frac{21}{8}\).