共50条信息
先化简，再求值：\((\dfrac{1}{x-y}-\dfrac{1}{x+y})\div \dfrac{2y}{{{x}^{2}}+2xy+{{y}^{2}}}\)，其中\(x=\sqrt{3}+\sqrt{2},\) \(y=\sqrt{3}-\sqrt{2}\)．
若记\(y=f(x)=\dfrac{x^{2}}{1{+}x^{2}}\)，则\(f(1)\)表示当\(x=1\)时\(y\)的值，即\(f(1)=\dfrac{1^{2}}{1{+}1^{2}}=\dfrac{1}{2}\)；\(f\left( \dfrac{1}{2} \right)\)表示当\(x=\dfrac{1}{2}\)时\(y\)的值，即\(f\left( \dfrac{1}{2} \right){=}\dfrac{\left( \dfrac{1}{2} \right)^{2}}{1{+}\left( \dfrac{1}{2} \right)^{2}}{=}\dfrac{1}{5}……\)求\(f(1)+f(2)+f\left( \dfrac{1}{2} \right)+f(3)+f\left( \dfrac{1}{3} \right)+f(4)+f\left( \dfrac{1}{4} \right)+…+f(2 018)+f\left( \dfrac{1}{2\ 018} \right)=\)__________．
已知\(\dfrac{{ab}}{a{+}b}{=}2{,}\dfrac{{bc}}{b{+}c}{=}3{,}\dfrac{{ac}}{a{+}c}{=}1{,}\)则\(\dfrac{{abc}}{ab{+}bc{+}ac}{=}\)__________．
先化简，再求值：\((\dfrac{x^{2}{-}2x{+}4}{x{-}1}{+}2{-}x){÷}\dfrac{x^{2}{+}4x{+}4}{1{-}x}\)，其中\(x\)满足\(x^{2}{-}4x{+}3{=}0\)．
先化简，再求值：\(\left( a+2+\dfrac{1}{a} \right)\div \left( a-\dfrac{1}{a} \right)\)，请你选择一个你喜欢、且符合条件的整数作为\(a\)的值代入化简后的式中计算．
先化简，再求值：
\(( \dfrac{a-1}{{a}^{2}-4a+4} - \dfrac{a+2}{{a}^{2}-2a} )÷( \dfrac{4}{a} -1)\)，其中\(a=2- \sqrt{3} \)．
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