7: \(\dfrac{1}{x+5}-\dfrac{1}{x-5}+\dfrac{2x}{x^2-25}\)
\(=\dfrac{1}{x+5}-\dfrac{1}{x-5}+\dfrac{2x}{\left(x-5\right)\left(x+5\right)}\)
\(=\dfrac{x-5-x-5+2x}{\left(x-5\right)\left(x+5\right)}=\dfrac{2x-10}{\left(x-5\right)\left(x+5\right)}=\dfrac{2}{x+5}\)
8: \(\dfrac{x}{x-1}-\dfrac{x}{x+1}+\dfrac{2}{x^2-1}\)
\(=\dfrac{x\left(x+1\right)-x\left(x-1\right)+2}{\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{x^2+x-x^2+x+2}{\left(x-1\right)\left(x+1\right)}=\dfrac{2x+2}{\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{2\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}=\dfrac{2}{x-1}\)
9: \(\dfrac{1}{x}+\dfrac{1}{x+7}+\dfrac{x-1}{x\left(x+7\right)}\)
\(=\dfrac{x+7+x+x-1}{x\left(x+7\right)}\)
\(=\dfrac{3x+6}{x\left(x+7\right)}\)
10: \(\dfrac{x}{2a-b}-\dfrac{4ax}{4a^2-b^2}+\dfrac{b}{2a+b}\)
\(=\dfrac{x}{2a-b}-\dfrac{4ax}{\left(2a-b\right)\left(2a+b\right)}+\dfrac{b}{2a+b}\)
\(=\dfrac{x\left(2a+b\right)-4ax+b\left(2a-b\right)}{\left(2a-b\right)\left(2a+b\right)}\)
\(=\dfrac{2xa+2bx-4ax+4ab-b^2}{\left(2a-b\right)\left(2a+b\right)}\)
\(=\dfrac{-2ax+2bx+4ab-b^2}{\left(2a-b\right)\left(2a+b\right)}\)
\(=\dfrac{-2ax+4ab+2bx-b^2}{\left(2a-b\right)\left(2a+b\right)}\)