知识点挑题 - 初中数学 - 优优班--学霸训练营

1．

计算

\((1){{(\sqrt{3}-\sqrt{2})}^{0}}-{{\left( -\dfrac{1}{2} \right)}^{2}}+{{2}^{-2}}-{{(-1)}^{3}}\) \((2)(\dfrac{1}{x-1}-\dfrac{1}{x+1})\div \dfrac{x}{2{{x}^{2}}-2}\)

难度：较难

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2．
先化简，再求值：\((\dfrac{1}{x-y}-\dfrac{1}{x+y})\div \dfrac{2y}{{{x}^{2}}+2xy+{{y}^{2}}}\)，其中\(x=\sqrt{3}+\sqrt{2},\) \(y=\sqrt{3}-\sqrt{2}\)．

难度：较难

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3．
计算：
\((1) \dfrac {a-2}{a+1}- \dfrac {2a-3}{a+1}\)
\((2)( \dfrac {2x}{x-3}- \dfrac {x}{x+3})⋅ \dfrac {x^{2}-9}{x}\)．

难度：较难

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4．
化简：\( \dfrac {x-2}{x+1}⋅(1+ \dfrac {2x+5}{x^{2}-4})\)

难度：较难

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5．
\((1)\)计算\((2017-π)^{0}-( \dfrac {1}{4})^{-1}+|-2|\)
\((2)\)化简\((1- \dfrac {1}{a-1})÷( \dfrac {a^{2}-4a+4}{a^{2}-a}).\)

难度：较难

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6．
\((1)\)计算：\(-1^{2015}-2^{3}÷(-2)+(- \dfrac {1}{3})^{0}- \sqrt {4}\)
\((2)\)化简：\( \dfrac {a-b}{a}÷(a- \dfrac {2ab-b^{2}}{a})\)．

难度：较难

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7．
化简
\((1) \dfrac {3a^{2}b}{6ab}\)
\((2) \dfrac {2a}{a^{2}-4}- \dfrac {1}{a+2}\)
\((3)[ \dfrac {a^{2}-1}{a^{2}-2a+1}- \dfrac {a}{a^{2}-a}]÷ \dfrac {a}{a-2}\)．

难度：较难

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8．
计算：\( \dfrac {x-y}{x}÷(x- \dfrac {2xy-y^{2}}{x})=\) ______ ．

难度：较难

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9．
化简或解方程：
\((1) \dfrac {x^{2}-1}{x^{2}+2x}÷ \dfrac {x-1}{x}\)
\((2) \dfrac {x^{2}}{x-1}-x-1\)
\((3) \dfrac {2x}{x-2}- \dfrac {2}{2-x}=1\)．

难度：较难

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10．
\({{(\dfrac{2a}{a-2})}^{3}}\cdot \dfrac{3{{a}^{2}}-12a+12}{-a}\div {{(-2a)}^{2}}\)

难度：较难

解析收藏试题篮

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