【答案】
分析:(1)在方程兩邊都除以3,然后把常數(shù)項移到方程的右邊,兩邊加上1后右邊變?yōu)橥耆椒绞�,左邊為非負常�?shù),開方后即可求出方程的解;
(2)先把括號中通分,利用同分母分式的加法法則計算,然后利用分式的除法法則變?yōu)槌朔ㄟ\算,分解因式后約分即可把原式化簡.
解答:解:(1)3x
2-6x-1=0,
方程兩邊除以3得:x
2-2x-
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=0,
移項得:x
2-2x=
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,
兩邊加上1得:x
2-2x+1=
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,即(x-1)
2=
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,
開方得:x-1=
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或x-1=-
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,
∴方程的解為:x
1=
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,x
2=
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;
(2)
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=
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•
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=x+1.
點評:此題考查了利用配方法解一元二次方程以及分式的混合運算.配方法的步驟是:先把二次項的系數(shù)化為1,常數(shù)項移項到方程右邊,然后方程兩邊加上一次項系數(shù)一半的平方,利用直接開平方的方法求出解;分式的加減運算主要運用分式的通分運算,分式的乘除運算主要運用分式的約分運算,學生在約分時要注意多項式能分解因式一定要先分解因式再約分.