Final answer:
To solve for x in the equation 1/q+p+x = 1/p + 1/q + 1/x, we can start by multiplying both sides of the equation by the least common denominator, which is pqx. Then, we can combine like terms and cancel out qx to isolate x. The final solution is x = pq(p + q)/2pq.
Step-by-step explanation:
To solve for x, we can start by multiplying both sides of the equation by the least common denominator, which is pqx. This will eliminate the denominators. The equation becomes (1)(pqx) + (pq)(p) + (pq)(q) = (pq)(p) + (pq)(q) + (pq)(x).
Simplifying, we get qx + pq + pq = pqp + pqq + qx.
Next, we can combine like terms on both sides of the equation. On the left side, qx + 2pq = pqp + pqq + qx. On the right side, qx + 2pq = pq(p + q) + qx.
Since qx is present on both sides of the equation, we can cancel it out. This leaves us with 2pq = pq(p + q).
Finally, we can solve for x by isolating it. Dividing both sides of the equation by 2pq, we get x = pq(p + q)/2pq.