`a!=p , b!=q,c!=r` and `|(p,b,c),(a,q,c),(a,b,r)|=0` the value of `p/(p-a)+q/(q-b)+r/(r-c)=`

Explanation

We have given, `|(p,b,c),(a,q,c),(a,b,r)|=0`

Now apply `R_1->R_1-R_2,R_2->R_2-R_3`

`|(p-a,b-q,c),(a,q-b,c-r),(a,b,r)|=0`

`implies (p−a)[r(q−b)−b(c−r)]−(b−q)[−a(c−r)]=0`

`implies r(p−a)(q−b)+b(p−a)(r−c)+a(q−b)(r−c)=0`

`implies r/(r-c)=b/(q-b)-a/(p-a)=0`

Now take `p/(p-a)+q/(q-b)+r/(r-c)`

`p/(p-a)+q/(q-b)-b/(q-b)-a/(p-a)`

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