1/p+1/q+1/x=1/p+q+x ; x not = 0 p not = 0 q not = 0 solve for x
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1/p+1/q+1/x=1/p+q+x
1/p+1/q=1/p+q+x-1/x
(q+p)/pq=x-p-q-x/(p+q+x)x
p+q/pq=-(p+q)/px+qx+x^2
1/pq=-1/px+qx+x^2
x^2+ px+qx=-pq
x^2+ px+qx+pq=0
x(x+p)+q(x+p)=0
(x+p)(x+q)=0
x=-p,x=-q
1/p+1/q=1/p+q+x-1/x
(q+p)/pq=x-p-q-x/(p+q+x)x
p+q/pq=-(p+q)/px+qx+x^2
1/pq=-1/px+qx+x^2
x^2+ px+qx=-pq
x^2+ px+qx+pq=0
x(x+p)+q(x+p)=0
(x+p)(x+q)=0
x=-p,x=-q
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hope it helps
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