Analyzing The Matrix

Algebra Level 5

\[\large \det\begin{pmatrix} p & b & c\\ a & q & c\\ a & b & r\\ \end{pmatrix}=0\]

In the determinant above \(a\neq p , b\neq q , c\neq r\), find the value of \(\dfrac{p}{p-a}+\dfrac{q}{q-b}+\dfrac{r}{r-c}\).