1.1+a 1+b 1+c ---------- + ------------ + ------------(a-b)(a-c) (b-c)(b-a) (c-a)(c-b)2.1 6 (x-1)------ - ------ - --------( x-3 ) (x²-9) (6+2x)3.进水管单独进水a小时可注满一池水,放水管单独放水b小时可把一池水放完(b>
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![1.1+a 1+b 1+c ---------- + ------------ + ------------(a-b)(a-c) (b-c)(b-a) (c-a)(c-b)2.1 6 (x-1)------ - ------ - --------( x-3 ) (x²-9) (6+2x)3.进水管单独进水a小时可注满一池水,放水管单独放水b小时可把一池水放完(b>](/uploads/image/z/1832082-42-2.jpg?t=1.1%2Ba+1%2Bb+1%2Bc+----------+%2B+------------+%2B+------------%28a-b%29%28a-c%29+%28b-c%29%28b-a%29+%28c-a%29%28c-b%292.1+6+%28x-1%29------+-+------+-+--------%28+x-3+%29+%28x%26sup2%3B-9%29+%286%2B2x%293.%E8%BF%9B%E6%B0%B4%E7%AE%A1%E5%8D%95%E7%8B%AC%E8%BF%9B%E6%B0%B4a%E5%B0%8F%E6%97%B6%E5%8F%AF%E6%B3%A8%E6%BB%A1%E4%B8%80%E6%B1%A0%E6%B0%B4%2C%E6%94%BE%E6%B0%B4%E7%AE%A1%E5%8D%95%E7%8B%AC%E6%94%BE%E6%B0%B4b%E5%B0%8F%E6%97%B6%E5%8F%AF%E6%8A%8A%E4%B8%80%E6%B1%A0%E6%B0%B4%E6%94%BE%E5%AE%8C%28b%3E)
1.1+a 1+b 1+c ---------- + ------------ + ------------(a-b)(a-c) (b-c)(b-a) (c-a)(c-b)2.1 6 (x-1)------ - ------ - --------( x-3 ) (x²-9) (6+2x)3.进水管单独进水a小时可注满一池水,放水管单独放水b小时可把一池水放完(b>
1.1+a 1+b 1+c
---------- + ------------ + ------------
(a-b)(a-c) (b-c)(b-a) (c-a)(c-b)
2.1 6 (x-1)
------ - ------ - --------
( x-3 ) (x²-9) (6+2x)
3.进水管单独进水a小时可注满一池水,放水管单独放水b小时可把一池水放完(b>a),
现在两个水管同时进水和放水,注满一池水需要多少小时?
1.2题把分式化简,第三题就列出式子再化简.
1.1+a 1+b 1+c ---------- + ------------ + ------------(a-b)(a-c) (b-c)(b-a) (c-a)(c-b)2.1 6 (x-1)------ - ------ - --------( x-3 ) (x²-9) (6+2x)3.进水管单独进水a小时可注满一池水,放水管单独放水b小时可把一池水放完(b>
1.(1+a)/ (a-b)(a-c)+ (1+b )/(b-c)(b-a)+ (1+c)/ (c-a)(c-b)
=(1+a)(b-c)/ (a-b)(b-c)(a-c)+ (1+b) (c-a)/(b-c)(b-a) (c-a)+ (1+c)(a-b)/ (c-a)(c-b)(a-b)
=(1+a)(b-c)/ (a-b)(b-c)(a-c)+ (1+b) (c-a)/(a-b)(b-c)(a-c)+ (1+c)(a-b)/ (a-b)(b-c)(a-c)
=[(1+a)(b-c)+(1+b) (c-a)+ (1+c)(a-b)]/ (a-b)(b-c)(a-c)
=[b-c+ab-ac+c-a+bc-ba+ a-b+ca-cb]/ (a-b)(b-c)(a-c)
=0/ (a-b)(b-c)(a-c)=0
2.1/ ( x-3 ) -6/ (x²-9)-(x-1)/ (6+2x)
= 1/ ( x-3 ) -6/( x-3 )( x+3 )-(x-1)/2 (x+3)
=2 (x+3) /2 (x+3) ( x-3 )-2*6/2 (x+3) ( x-3 )-(x-1)( x-3 )/2 (x+3) ( x-3 )
=[2 (x+3) -2*6-(x-1)( x-3 )]/2 (x+3) ( x-3 )
=[2x+6 -12-(x^2-4x+3 )]/2 (x+3) ( x-3 )
=(-x^2+6x-9)/2 (x+3) ( x-3 )
=-(x-3)^2/2 (x+3) ( x-3 )
=(3-x)/2 (x+3)
3.进水管单独进水a小时可注满一池水,放水管单独放水b小时可把一池水放完(b>a),
现在两个水管同时进水和放水,注满一池水需要多少小时?
根据题意,注满水的时间应为
1/(1/a-1/b)=1/(b/ab-a/ab)=1/(b-a)/ab=ab/(b-a)
这个是要算么?
1.通分得 (1+a)(b-c)-(1+b)(a-c)+(1+c)(a-b)
————————————————
(a-b)(a-c)(b-c)
化简为b-c+ab-ac-a+c-ab+bc+a-b+ac-bc
————...
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1.通分得 (1+a)(b-c)-(1+b)(a-c)+(1+c)(a-b)
————————————————
(a-b)(a-c)(b-c)
化简为b-c+ab-ac-a+c-ab+bc+a-b+ac-bc
————————————————
(a-b)(a-c)(b-c)
=0
2.通分得 2(X+3)-6-(X-3)
——————————
2(X+3)(X-3)
化简 2X+6-6-X+3 X+3 1
—————————= ——————— = ———
2(X+3)(X-3) 2(X+3)(X-3) 2(X-3)
3. 设水池容积为V,则
进水速度为V/a,放水速度为V/b,
两水管同时进放水的速度为V/a-V/b,
那么需要的时间为V/(V/a-V/b)
V ab
———————— = ————
Vb-Va a-b
--------
ab
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