Let $a,$ $b,$ $c,$ $p,$ $q,$ and $r$ be real numbers such that
\[\begin{vmatrix} p & b & c \\ a & q & c \\ a & b & r \end{vmatrix} = 0.\]Assuming that $a \neq p,$ $b \neq q,$ and $c \neq r,$ find the value of $\frac{p}{p - a} + \frac{q}{q - b} + \frac{r}{r - c}.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $a,$ $b,$ $c,$ $p,$ $q,$ and $r$ be real numbers such that
\[\begin{vmatrix} p & b & c \\ a & q & c \\ a & b & r \end{vmatrix} = 0.\]Assuming that $a \neq p,$ $b \neq q,$ and $c \neq r,$ find the value of $\frac{p}{p - a} + \frac{q}{q - b} + \frac{r}{r - c}.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
2
Let $a,$ $b,$ $c,$ $p,$ $q,$ and $r$ be real numbers such that
\[\begin{vmatrix} p & b & c \\ a & q & c \\ a & b & r \end{vmatrix} = 0.\]Assuming that $a \neq p,$ $b \neq q,$ and $c \neq r,$ find the value of $\frac{p}{p - a} + \frac{q}{q - b} + \frac{r}{r - c}.$
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