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\(A=\left(\frac{x-2}{x+2}-\frac{x+2}{2-x}-\frac{x^2-3x+6}{x^2-4}\right):\left(1-\frac{3}{x-2}\right)\)
\(=\left(\frac{\left(x-2\right)^2}{\left(x+2\right)\left(x-2\right)}+\frac{\left(x+2\right)^2}{\left(x+2\right)\left(x-2\right)}-\frac{x^2-3x+6}{\left(x-2\right)\left(x+2\right)}\right)\)\(:\left(\frac{x-2}{x-2}-\frac{3}{x-2}\right)\)
\(=\frac{x^2-4x+4+x^2+4x+4-x^2+3x-6}{\left(x+2\right)\left(x-2\right)}:\frac{x-2-3}{x-2}\)
\(=\frac{x^2+3x+2}{\left(x+2\right)\left(x-2\right)}:\frac{x-5}{x-2}\)
\(=\frac{x^2+x+2x+2}{\left(x+2\right)\left(x-2\right)}:\frac{x-5}{x-2}\).
\(=\frac{x\left(x+1\right)+2\left(x+1\right)}{\left(x+2\right)\left(x-2\right)}.\frac{x-2}{x-5}\)
\(=\frac{\left(x+2\right)\left(x+1\right)}{\left(x+2\right)\left(x-2\right)}.\frac{x-2}{x-5}\)
\(=\frac{x+1}{x-2}.\frac{x-2}{x-5}\)
\(=\frac{x+1}{x-5}\)
.
\(=3x^3-\frac{3}{2}x^2-x^3-\frac{1}{2}x+\frac{1}{2}x+2\)
\(=2x^3-\frac{3}{2}x^2+2\)
ĐK: x khác +-2
\(C=\left(\frac{2}{x+2}-\frac{x}{\left(x-2\right)\left(x+2\right)}+\frac{1}{x-2}\right).\left(\frac{x-2}{x^2-4+6-x^2}\right)\\ \)
\(C=\frac{2\left(x-2\right)-x+\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}.\left(\frac{x-2}{2}\right)=\frac{2\left(x-1\right)\left(x-2\right)}{2.\left(x-2\right)\left(x+2\right)}\)
\(C=\frac{x-1}{x+2}\)
C=[2/(x+2)-x/(x^2-4)-1/(2-x)]:[x+2+(6-x^2)/(x-2)]
=[2/(x+2)-x/(x-2)(x+2)-(-1)/(x-2)]:[x+2+(6-x^2)/(x-2)]
=[2x-4-x+x+2/(x-2)(x+2)]:[(x^2-4+6-x^2)/(x-2)]
=2x-2/(x-2)(x+2) . (x-2)/2
=2(x-1)/(x-2)(x+2) . (x-2)/2
=x-1/x+2