SOLVE FOR X: 1/p+q+x = 1/p + 1/q + 1/x , x isnot equal to -(p+q)
and why do they give at last that x isn't equal to......??

  1/p+1/q+1/x=1/p+q+x
1/p + 1/q = 1/p+q+x - 1/x
{(p+q) / pq }={[x -(p+q+x)]/x(p+q+x)}
{(p+q) / pq }={[x -p-q- x)]/x(p+q+x)}
{(p+q) / pq }={[x -p-q-x)]/x(p+q+x)}
{ (p+q) / pq }={[- (p+q) ] /x(p+q+x)}
{(p+q) / pq }={[-(p+q)]/x(p+q+x)}
{1 /pq} = {-1/x(p+q+x) }
Cross multiply :
-pq = x(p+q+x)
x(p+q+x)+pq = 0
px+qx+x² +pq = 0
x² +x(p+q)+pq =0 
By Applying splitting the middle term :
x²+px+qx+pq = 0
x(x+p)+q(x+p) = 0
(x+p){x+q} =0
(x+p)(x+q) = 0
So:
(x+p)=0  , (x+q)=0
x= -p  , x= -q
The values of "x" = -p and -q