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Question

Solve for x
(1p)+(1q)+(1x)=1(x+p+q)

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Solution

The given equation

1p+1q+1x=1p+q+x

1p+1q=1p+q+x1x

p+qpq=x(p+q+x)x(p+q+x)

p+qpq=(p+q)x(p+q+x)

Dividing by p+q on the both sides of the equation:

1pq=1x(p+q+x)

x(p+q+x)=pq

x2+px+qx+pq=0

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

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

therefore
x=p or x=q


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