知识点挑题 - 初中数学 - 优优班--学霸训练营

1．
计算\( \dfrac {b}{a^{2}-b^{2}}÷(1- \dfrac {a}{a+b})\)的结果是 ______ ．

难度：较易

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2．
\((1)\)计算：\( \sqrt {4}+2017^{0}-| \sqrt {3}-2|+1\)；
\((2)\)计算：\( \dfrac {x^{2}+4x+4}{x^{2}+2x}÷(2x- \dfrac {4+x^{2}}{x})\)．

难度：较易

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3．
计算：
\((1) \dfrac {x^{2}+6xy+9y^{2}}{x^{2}-9y^{2}}\)
\((2) \dfrac {x^{2}}{6y}\cdot ( \dfrac {3y}{x})^{2}\)
\((3) \dfrac {b^{2}}{4a}÷ \dfrac {b}{2a^{2}}\)
\((4) \dfrac {x-2}{x+2}+ \dfrac {8x}{x^{2}-4}\)

难度：较易

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4．
计算：\(( \dfrac {5}{x-2}-x-2)÷ \dfrac {x^{2}-6x+9}{x-2}+ \dfrac {x}{x-3}\)．

难度：难

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5．
计算：
\((1) \sqrt {18}- \dfrac {2}{ \sqrt {2}}+|1- \sqrt {2}|\)
\((2)1- \dfrac {x^{2}-9}{x^{2}-6x+9}÷ \dfrac {x+3}{x+4}\)．

难度：较易

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6．
化简：
\((1)(x-y)(3x-y)-(x-2y)^{2}+5y^{2}\)
\((2) \dfrac {1}{y}- \dfrac {y-3}{y-2}÷(y+2- \dfrac {5}{y-2})\)．

难度：较易

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7．
化简下列各式：
\((1)(2a-1)(1+2a)-(a-2)(a+3)-(a-1)^{2}\)；
\((2) \dfrac {x-1}{x^{2}-9}÷( \dfrac {x}{x-3}- \dfrac {5x-1}{x^{2}-9})- \dfrac {1}{x+1}\)．

难度：较易

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8．
化简\( \dfrac {x^{2}+x}{x^{2}-2x+1}÷( \dfrac {2}{x-1}- \dfrac {1}{x})\)的结果是 ______ ．

难度：较易

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9．
\((1)3^{-1}-\sin 45^{\circ}+( \sqrt {2}-1)^{0}+|- \dfrac { \sqrt {2}}{2}|\)；
\((2)( \dfrac {a}{a-1}- \dfrac {1}{a+1})÷ \dfrac {1}{a^{2}-1}\)．

难度：易

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10．
计算
\((1) \dfrac {3}{ \sqrt {3}}-( \sqrt {3})^{2}+(π+ \sqrt {3})^{0}- \sqrt {27}+| \sqrt {3}-2|\)
\((2)(3 \sqrt {12}-2 \sqrt { \dfrac {1}{3}}+ \sqrt {48})÷2 \sqrt {3}\)
\((3)(2 \sqrt {5}+ \sqrt {3})^{2}-( \sqrt {5}+ \sqrt {2})( \sqrt {5}- \sqrt {2})\)
\((4) \dfrac {a^{2}-1}{a^{2}-2a+1}+ \dfrac {2a-a^{2}}{a-2}÷a\)．

难度：易

解析收藏试题篮

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