# Solve 1/P + 1/Q + 1/X = 1/(X + P + Q) - Mathematics

Sum

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

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#### APPEARS IN

Selina Concise Maths Class 10 ICSE