a) \(P=\left(\dfrac{x-1}{x-3}+\dfrac{x-3}{x+3}+\dfrac{4x-2}{x^2-9}\right):\left(1-\dfrac{x+1}{x+3}\right).\) \(\left(ĐKXĐ:x\ne3;x\ne-3\right).\)
\(P=\left(\dfrac{x-1}{x-3}+\dfrac{x-3}{x+3}+\dfrac{4x-2}{\left(x-3\right)\left(x+3\right)}\right):\dfrac{x+3-x-1}{x+3}.\)
\(P=\dfrac{\left(x-1\right)\left(x+3\right)+\left(x-3\right)^2+4x-2}{\left(x-3\right)\left(x+3\right)}.\dfrac{x+3}{2}.\)
\(P=\dfrac{x^2+3x-x-3+x^2-6x+9+4x-2}{x-3}.\dfrac{1}{2}.\)
\(P=\dfrac{2x^2+4}{x-3}.\dfrac{1}{2}=\dfrac{2\left(x^2+2\right)}{x-3}.\dfrac{1}{2}=\dfrac{x^2+2}{x-3}.\)
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