\(đk:x\ne7;-7\\ =\dfrac{x+7}{x-7}-\dfrac{x-7}{x+7}+\dfrac{4x^2}{\left(x-7\right)\left(x+7\right)}\\ =\dfrac{\left(x+7\right)^2-\left(x-7\right)^2+4x^2}{\left(x-7\right)\left(x+7\right)}\\ =\dfrac{x^2+14x+49-x^2+14x-49+4x^2}{\left(x-7\right)\left(x+7\right)}\\ =\dfrac{4x^2+28x}{\left(x-7\right)\left(x+7\right)}\\ =\dfrac{4x\left(x+7\right)}{\left(x-7\right)\left(x+7\right)}\\ =\dfrac{4x}{x-7}\)
\(\dfrac{x+7}{x-7}-\dfrac{x-7}{x+7}+\dfrac{4x^2}{x^2-49}\left(x\ne\pm7\right)\)
\(=\dfrac{\left(x+7\right)^2}{x^2-49}-\dfrac{\left(x-7\right)^2}{x^2-49}+\dfrac{4x^2}{x^2-49}\)
\(=\dfrac{x^2+14x+49-x^2+14x-49+4x^2}{x^2-49}\)
\(=\dfrac{4x^2+28x}{x^2-49}=\dfrac{4x\left(x+7\right)}{\left(x+7\right)\left(x-7\right)}=\dfrac{4x}{x-7}\)
\(\dfrac{x+7}{x-7}-\dfrac{x-7}{x+7}+\dfrac{4x^2}{x^2-49}\\ =\dfrac{x+7}{x-7}-\dfrac{x-7}{x+7}+\dfrac{4x^2}{\left(x-7\right)\left(x+7\right)}\)
\(=\dfrac{\left(x+7\right)^2}{\left(x-7\right)\left(x+7\right)}-\dfrac{\left(x-7\right)^2}{\left(x-7\right)\left(x+7\right)}+\dfrac{4x^2}{\left(x-7\right)\left(x+7\right)}\)
\(=\dfrac{x^2+14x+49-x^2+14x-49+4x^2}{\left(x-7\right)\left(x+7\right)}\)
\(=\dfrac{x^2-x^2+4x^2+14x+14x+49-49}{\left(x-7\right)\left(x+7\right)}\)
\(=\dfrac{4x^2+28x}{\left(x-7\right)\left(x+7\right)}\)
\(=\dfrac{4x\left(x+7\right)}{\left(x-7\right)\left(x+7\right)}\\ =\dfrac{4x}{x-7}\)