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 $\dfrac{p}{p-a}+\dfrac{q}{q-b}+\dfrac{r}{r-c}$ .