\(\sqrt{\dfrac{x+7}{x-7}}-\sqrt{\dfrac{x-7}{x+7}}\)
\(=\sqrt{\dfrac{\left(x+7\right)^2}{\left(x-7\right)\left(x+7\right)}}-\sqrt{\dfrac{\left(x-7\right)^2}{\left(x+7\right)\left(x-7\right)}}\)
\(=\dfrac{\sqrt{\left(x+7\right)^2}-\sqrt{\left(x-7\right)^2}}{\sqrt{x^2-49}}\)
\(=\dfrac{\left|x+7\right|-\left|x-7\right|}{\sqrt{x^2-49}}\)
\(=\dfrac{x+7-x+7}{\sqrt{x^2-49}}=\dfrac{14\sqrt{x^2-49}}{x^2-49}\)
=>m=14