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

Solve the equation \( \frac{1}{p}+\frac{2}{p+4}=\frac{5}{p} \). Solve the equation by following steps: - step0: Solve for \(p\): \(\frac{1}{p}+\frac{2}{p+4}=\frac{5}{p}\) - step1: Find the domain: \(\frac{1}{p}+\frac{2}{p+4}=\frac{5}{p},p \in \left(-\infty,-4\right)\cup \left(-4,0\right)\cup \left(0,+\infty\right)\) - step2: Multiply both sides of the equation by LCD: \(\left(\frac{1}{p}+\frac{2}{p+4}\right)p\left(p+4\right)=\frac{5}{p}\times p\left(p+4\right)\) - step3: Simplify the equation: \(3p+4=5p+20\) - step4: Move the expression to the left side: \(3p-5p=20-4\) - step5: Add and subtract: \(-2p=20-4\) - step6: Add and subtract: \(-2p=16\) - step7: Change the signs: \(2p=-16\) - step8: Divide both sides: \(\frac{2p}{2}=\frac{-16}{2}\) - step9: Divide the numbers: \(p=-8\) - step10: Check if the solution is in the defined range: \(p=-8,p \in \left(-\infty,-4\right)\cup \left(-4,0\right)\cup \left(0,+\infty\right)\) - step11: Find the intersection: \(p=-8\) The solution to the equation \( \frac{1}{p}+\frac{2}{p+4}=\frac{5}{p} \) is \( p=-8 \).