Question

solve each equation. remember to ch

1. $\frac{1}{p^2} - \frac{1}{p} = \frac{2}{p}$

Explanation:

Step1: Eliminate denominators (p≠0)

Multiply all terms by \( p^2 \) to get \( 1 - p = 2p \).

Step2: Solve for p

Add \( p \) to both sides: \( 1 = 3p \). Then divide by 3: \( p = \frac{1}{3} \).

Step3: Check solution

Substitute \( p = \frac{1}{3} \) into original equation:
Left: \( \frac{1}{(\frac{1}{3})^2} - \frac{1}{\frac{1}{3}} = 9 - 3 = 6 \).
Right: \( \frac{2}{\frac{1}{3}} = 6 \). Both sides equal, so valid.

Answer:

\( p = \frac{1}{3} \)