Question

1/(x+p+q) = 1/x+1/p+1/q.find x​

Answer 1

Here you go.......

=> 1/p + 1/q = 1/(p+q+x) - 1/x 

=> (q+p) / (pq) = {x -(p+q+x)} / {(p+q+x).x} 

=> (p+q) / (pq) = - (p+q) / {(p+q+x).x} 

=> 1/(pq) = -1 / {(p+q+x).x} (since, p+q ≠ 0)

=> (p+q+x).x = - pq 

=> px +qx + x² + pq = 0 

=> x² + px + qx + pq = 0 

=> x ( x + p ) + q ( x + p ) = 0 

=> ( x + p ) . ( x + q ) = 0 

=> x + p = 0 OR x + q = 0 

Hence, x = -p OR -q _______ ( Ans. )

Hope it helps.

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