a) ĐKXĐ:
\(x^2+4x-5\ne0\Leftrightarrow x\ne1;x\ne-5\)
\(1-x\ne0\Leftrightarrow x\ne1\)
\(x+5\ne0\Leftrightarrow x\ne-5\)
\(x^3-1\ne0\Leftrightarrow x\ne1\)
\(\dfrac{7x-14}{x^3-1}\ne0\Leftrightarrow7x-14\ne0\Leftrightarrow x\ne2\)
\(A=\left(\dfrac{9-3x}{x^2+4x-5}-\dfrac{x+5}{1-x}-\dfrac{x+1}{x+5}\right):\dfrac{7x-14}{x^3-1}\)
\(=\left[\dfrac{9-3x}{\left(x-1\right)\left(x+5\right)}+\dfrac{x+5}{x-1}-\dfrac{x+1}{x+5}\right]\cdot\dfrac{x^3-1}{7\left(x-2\right)}\)
\(=\dfrac{9-3x+\left(x+5\right)^2-\left(x+1\right)\left(x-1\right)}{\left(x-1\right)\left(x+5\right)}\cdot\dfrac{x^3-1}{7\left(x-2\right)}\)
\(=\dfrac{9-3x+x^2+10x+25-x^2+1}{\left(x-1\right)\left(x+5\right)}\cdot\dfrac{x^3-1}{7\left(x-2\right)}\)
\(=\dfrac{7x+35}{\left(x-1\right)\left(x+5\right)}\cdot\dfrac{x^3-1}{7\left(x-2\right)}\)
\(=\dfrac{7\left(x+5\right)\left(x-1\right)\left(x^2+x+1\right)}{7\left(x+5\right)\left(x-1\right)\left(x-2\right)}\)
\(=\dfrac{x^2+x+1}{x-2}\)
