23 trên 59 cộng 9 trên 45 cộng 36 trên 59 cộng 4 trên 5
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Một vận động viên xe đạp đua đi ba chặng đường hết tất cả 8h40ph trạng một hết 2h40p trạng hai mất ít hơn chạm bốn 1,45ph hỏi trạm ba đi mất bao nhiêu phút ?
Ai giúp mk với
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{8.9.10}\right).x=\frac{23}{45}\)
\(\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{8.9}-\frac{1}{9.10}\right).x=\frac{23}{45}\)
\(\left(\frac{1}{1.2}-\frac{1}{9.10}\right).x=\frac{23}{45}\)
\(\frac{22}{45}.x=\frac{23}{45}\)
\(x=\frac{23}{45}:\frac{22}{45}\)
\(x=\frac{23}{22}\)
\(\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{8.9.10}\right)x=\frac{23}{45}\)
\(\Rightarrow\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{8.9.10}\right).\frac{x}{2}=\frac{23}{45}\)
\(\Rightarrow\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{8.9}-\frac{1}{9.10}\right)x=\frac{46}{45}\)
\(\Rightarrow\left(\frac{1}{1.2}-\frac{1}{9.10}\right)x=\frac{46}{45}\)
\(\Rightarrow\frac{22}{45}.x=\frac{46}{45}\Rightarrow x=\frac{46}{22}=\frac{23}{11}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1: \(\dfrac{x-3}{x+1}=\dfrac{x^2}{x^2-1}\)
=>(x-3)(x-1)=x^2
=>x^2=x^2-4x+3
=>-4x+3=0
=>x=3/4
2: \(\dfrac{5}{3x+2}=2x-1\)
=>(2x-1)(3x+2)=5
=>6x^2+4x-3x-2-5=0
=>6x^2+x-7=0
=>6x^2+7x-6x-7=0
=>(6x+7)(x-1)=0
=>x=1hoặc x=-7/6
![](https://rs.olm.vn/images/avt/0.png?1311)
\(17\times109-17\times53+56\times96-13\times56\)
\(=17\times\left(109-53\right)+56\times\left(96-13\right)\)
\(=17\times56+56\times83\)
\(=56\times\left(17+83\right)\)
\(=56\times100\)
\(=5600\)
\(8\times27\times3+2\times31\times12+6\times12\times4\)
\(=24\times27+24\times31+24\times12\)
\(=24\times\left(27+31+12\right)\)
\(=24\times70\)
\(=1680\)
\(15\times47+15\times33+60\times39+60\times41\)
\(=15\times\left(47+33\right)+60\times\left(39+41\right)\)
\(=15\times80+60\times80\)
\(=80\times\left(15+60\right)\)
\(=80\times75\)
\(=6000\)
\(97\times59-59\times31-66\times49\)
\(=59\times\left(97-31\right)-66\times49\)
\(=59\times66-66\times49\)
\(=66\times\left(59-49\right)\)
\(=66\times10\)
\(=660\)
Học tốt
![](https://rs.olm.vn/images/avt/0.png?1311)
\(S=\frac{3}{5.7}+\frac{3}{7.9}+.....+\frac{3}{59.61}\)
\(=\frac{3}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+......+\frac{2}{59.61}\right)\)
=\(\frac{3}{2}.\left(\frac{7-5}{5.7}+\frac{9-7}{7.9}+......+\frac{61-59}{59.61}\right)\)
=\(\frac{3}{2}.\left(\frac{7}{5.7}-\frac{5}{5.7}+\frac{9}{7.9}-\frac{7}{7.9}+.....+\frac{61}{59.61}-\frac{59}{59.61}\right)\)
=\(\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+.....+\frac{1}{59}-\frac{1}{61}\right)\)
=\(\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{61}\right)\)
=\(\frac{3}{2}.\frac{56}{305}\)
=\(\frac{84}{305}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt A=\(\frac{1}{3}.5+\frac{1}{5}.7+...+\frac{1}{97}.99\)
=>A=\(\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{97.99}\)
=>2A=\(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{97.99}\)
=>2A=\(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}\)
=>2A=\(\frac{1}{3}-\frac{1}{99}=\frac{33}{99}-\frac{1}{99}=\frac{32}{99}\)
=>A=\(\frac{32}{99}:2=\frac{32}{99}.\frac{1}{2}=\frac{32}{198}=\frac{16}{99}\)
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