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Solve 1/P + 1/Q + 1/X = 1/(X + P + Q) - ICSE Class 10 - Mathematics

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Question

Solve `1/p + 1/q + 1/x = 1/(x + p + q)`

Solution

`1/p + 1/q + 1/x = 1/(x + p + q)`

`=> 1/p + 1/q + 1/x - 1/(x + p + 1) = 0`

`=> ((q + p)[1/(pq) + 1/(x^2 + px + qx)] = 0`

`=> (p + q) [(x^2 + px + qx + pq)/(pq(x^2 + px + qx))] = 0`

`=> x^2 + px + qx + pq = 0`

`=> x(x + p) + q(x + p) = 0`

`=> (x + p)(x + q) = 0`

=> x = -p and x = -q

  Is there an error in this question or solution?
Solution Solve 1/P + 1/Q + 1/X = 1/(X + P + Q) Concept: Solutions of Quadratic Equations by Factorization.
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