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If \( p_{1}, p_{2}, p_{3} \) are altitudes of a triangle \( A B C \) from the vertices \( A, B, C \) and \( \Delta \), the area of the triangle, then \( p_{1}^{-1}+p_{2}^{-1}-p_{3}^{-1} \) is equal to
(A) \( \frac{s-a}{\Delta} \)
(B) \( \frac{s-b}{\Delta} \)
(C) \( \frac{s-c}{\Delta} \)
(D) \( \frac{S}{\Delta} \)
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