\(d,\dfrac{5}{x+5}+\dfrac{2}{x-5}-\dfrac{3x-35}{x^2-25}=\dfrac{5\left(x-5\right)+2\left(x+5\right)-\left(3x-35\right)}{\left(x-5\right)\left(x+5\right)}=\dfrac{5x-25+2x+10-3x+35}{\left(x-5\right)\left(x+5\right)}=\dfrac{4x+20}{\left(x-5\right)\left(x+5\right)}=\dfrac{4\left(x+5\right)}{\left(x-5\right)\left(x+5\right)}=\dfrac{4}{x-5}\)
\(e,\dfrac{5}{x+3}-\dfrac{x-12}{x^2+3x}=\dfrac{5x}{x\left(x+3\right)}-\dfrac{x-12}{x\left(x+3\right)}=\dfrac{5x-x+12}{x\left(x+3\right)}=\dfrac{4x+12}{x\left(x+3\right)}=\dfrac{4\left(x+3\right)}{x\left(x+3\right)}=\dfrac{4}{x}\)
\(f,\dfrac{x}{x-1}-\dfrac{x}{x+1}+\dfrac{2}{x^2-1}=\dfrac{x\left(x+1\right)-x\left(x-1\right)+2}{\left(x-1\right)\left(x+1\right)}=\dfrac{x^2+x-x^2+x+2}{\left(x-1\right)\left(x+1\right)}=\dfrac{2x+2}{\left(x-1\right)\left(x+1\right)}=\dfrac{2\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}=\dfrac{2}{x-1}\)
