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Question
Solve:
`1/p + 1/q + 1/x = 1/(x + p + q)`
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Solution
`1/p + 1/q + 1/x = 1/(x + p + q)`
`=> 1/p + 1/q + 1/x - 1/(x + p + q) = 0`
`=> (q + p)[1/(pq) + 1/(x^2 + px + qx)] = 0`
`=> (p + q) [(x^2 + px + qx + pq)/(pq(x^2 + px + qx))] = 0`
`=>` x2 + px + qx + pq = 0
`=>` x(x + p) + q(x + p) = 0
`=>` (x + p)(x + q) = 0
`=>` x = – p and x = – q
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