f. \( \frac{1}{p}+\frac{2}{p+4}=\frac{5}{p} \)

To solve the equation \( \frac{1}{p}+\frac{2}{p+4}=\frac{5}{p} \), we can start by first eliminating the fractions. Multiply each term by \( p(p + 4) \) to get rid of the denominators: \[ p(p + 4)\left(\frac{1}{p}\right) + p(p + 4)\left(\frac{2}{p + 4}\right) = p(p + 4)\left(\frac{5}{p}\right) \] This simplifies to: \[ (p + 4) + 2p = 5(p + 4) \] \[ p + 4 + 2p = 5p + 20 \] \[ 3p + 4 = 5p + 20 \] Next, we can rearrange the equation to isolate \( p \): \[ 4 - 20 = 5p - 3p \] \[ -16 = 2p \] \[ p = -8 \] Thus, the solution to the equation is \( p = -8 \).