Question: Solve for z. \[ \frac{5}{z} = \frac{13}{z} + 12 \] Simplify your answer as much as possible…

Solve for z. \[ \frac{5}{z} = \frac{13}{z} + 12 \] Simplify your answer as much as possible. z = [ ] No solution \sqrt{[ ]} \frac{[ ]}{[ ]} [ ]…

Solution

To solve for \( z \) in the equation: \[ \frac{5}{z} = \frac{13}{z} + 12 \] First, eliminate the fractions by multiplying every term by \( z \): \[ z \cdot \frac{5}{z} = z \cdot \frac{13}{z} + z \cdot 12 \] This simplifies to: \[ 5 = 13 + 12z \] Subtract 13 from both sides to isolate the term with \( z \): \[ 5 - 13 = 12z \] \[ -8 = 12z \] Divide both sides by 12 to solve for \( z \): \[ z = \frac{-8}{12} \] Simplify the fraction: \[ z = \frac{-2}{3} \] Thus, the solution is \( z = -\frac{2}{3} \).