Question

Cho biểu thức C = \(\left(\frac{2}{x+2}-\frac{x}{x^2-4}-\frac{1}{2-x}\right):\left(x+2+\frac{6-x^2}{x-2}\right)\)

Rút gọn biểu thức C

Answer 1

ĐK: x khác +-2 

\(C=\left(\frac{2}{x+2}-\frac{x}{\left(x-2\right)\left(x+2\right)}+\frac{1}{x-2}\right).\left(\frac{x-2}{x^2-4+6-x^2}\right)\\ \)

\(C=\frac{2\left(x-2\right)-x+\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}.\left(\frac{x-2}{2}\right)=\frac{2\left(x-1\right)\left(x-2\right)}{2.\left(x-2\right)\left(x+2\right)}\)

\(C=\frac{x-1}{x+2}\)

Answer 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