$\Leftrightarrow\dfrac{x+5}{x\left(x-5\right)}-\dfrac{x+25}{2\left(x+5\right)\left(x-5\right)}=\dfrac{x-5}{2x\left(x+5\right)}$
$\Leftrightarrow\dfrac{2\left(x+5\right)\left(x+5\right)}{2x\left(x-5\right)\left(x+5\right)}-\dfrac{x\left(x+25\right)}{2\left(x+5\right)\left(x-5\right)}=\dfrac{\left(x-5\right)\left(x-5\right)}{2x\left(x+5\right)\left(x-5\right)}$
$\Leftrightarrow2\left(x+5\right)^2-x^2-25x=\left(x-5\right)^2$
$\Leftrightarrow2\left(x^2+10x+25\right)-x^2-25x=x^2-10x+25$
$\Leftrightarrow2x^2+20x+50-x^2-25x-x^2+10x-25=0$
$\Leftrightarrow5x+25=0$
$\Leftrightarrow5\left(x+5\right)=0$
$\Leftrightarrow x=-5$ $($ loại $)$
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