Cho biểu thức A= ( x^3-1/ x-1+x)( x^3+1/ x+1 -x): x( 1-x^2)^2/ x^2-2 a)    Rút gọn biểu thức A

Trả lời

$\begin{array}{l}a)\left(\frac{x^3-1}{x-1}+x\right)\left(\frac{x^3+1}{x+1}-x\right):\frac{x{\left(1-x^2\right)}^2}{x^2-2}=\left(x^2+2x+1\right)\left(x^2-2x+1\right).\frac{x^2-2}{x{\left(1-x\right)}^2{\left(1+x\right)}^2}\\ ={\left(x+1\right)}^2{\left(x-1\right)}^2.\frac{x^2-2}{x{\left(1-x\right)}^2{\left(1+x\right)}^2}=\frac{x^2-2}{x}\\ b)x=\sqrt{6+2\sqrt{2}}(tm)\Rightarrow A=\frac{6+2\sqrt{2}-2}{\sqrt{6+2\sqrt{2}}}=\frac{2\sqrt{2}+2}{\sqrt{3+\sqrt{2}}}\end{array}$