1+3+61
K
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NP
1
VN
10 tháng 9 2017
12.194+6.437.2+3.369.4
=12.194+(6.2).437+(3.4).369
=12.194+12. 437+12.369
=12.(194+437+369)
=12.1000
=12000
5 tháng 11 2023
a: \(61\cdot45+61\cdot23-68\cdot51\)
\(=61\left(45+23\right)-68\cdot51\)
\(=68\cdot61-68\cdot51\)
\(=68\left(61-51\right)=68\cdot10=680\)
b: \(3\cdot5^2-\left(75-4\cdot2^3\right)\)
\(=75-75+4\cdot8\)
\(=4\cdot8=32\)
c: \(36:\left\{2^2\cdot5-\left[30-\left(5-1\right)^2\right]\right\}\)
\(=\dfrac{36}{20-30+4^2}\)
\(=\dfrac{36}{-10+16}=\dfrac{36}{6}=6\)
d: \(\left(12\cdot49-3\cdot2^2\cdot7^2\right):\left(2020\cdot2021\right)\)
\(=\dfrac{\left(12\cdot49-12\cdot49\right)}{2020\cdot2021}=0\)
18 tháng 11 2023
a: ĐKXĐ: \(x\notin\left\{4;-4\right\}\)
\(\dfrac{7}{4x+16}=\dfrac{7}{4\left(x+4\right)}=\dfrac{7\left(x-4\right)}{4\left(x+4\right)\left(x-4\right)}\)
\(\dfrac{11}{x^2-16}=\dfrac{11\cdot4}{4\left(x^2-16\right)}=\dfrac{44}{4\left(x-4\right)\left(x+4\right)}\)
b: \(\dfrac{6}{x\left(x+3\right)^2};\dfrac{x-3}{2x\left(x+3\right)^2}\)
ĐKXĐ: \(x\notin\left\{0;-3\right\}\)
\(\dfrac{6}{x\left(x+3\right)^2}=\dfrac{6\cdot2}{2x\left(x+3\right)^2}=\dfrac{12}{2x\left(x+3\right)^2}\)
\(\dfrac{x-3}{2x\left(x+3\right)^2}=\dfrac{x-3}{2x\left(x+3\right)^2}\)
c: \(\dfrac{-6}{1-x};\dfrac{3x}{x^2+x+1};\dfrac{x^2-3x+5}{x^3-1}\)
ĐKXĐ: \(x\ne1\)
\(-\dfrac{6}{1-x}=\dfrac{6}{x-1}=\dfrac{6\left(x^2+x+1\right)}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{6x^2+6x+6}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(\dfrac{3x}{x^2+x+1}=\dfrac{3x\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{3x^2-3x}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(\dfrac{x^2-3x+5}{x^3-1}=\dfrac{x^2-3x+5}{\left(x-1\right)\left(x^2+x+1\right)}\)
d: \(\dfrac{17}{5x};\dfrac{24}{x-2y};\dfrac{x-y}{8y^2-2x^2}\)
ĐKXĐ: \(x\ne0;x\ne\pm2y\)
\(\dfrac{17}{5x}=\dfrac{17\cdot2\left(x-2y\right)\left(x+2y\right)}{5x\cdot2\cdot\left(x-2y\right)\left(x+2y\right)}=\dfrac{34\left(x^2-4y^2\right)}{10x\left(x-2y\right)\left(x+2y\right)}\)
\(\dfrac{24}{x-2y}=\dfrac{24\cdot10x\left(x+2y\right)}{10x\left(x-2y\right)\left(x+2y\right)}=\dfrac{240x\left(x+2y\right)}{10x\left(x-2y\right)\left(x+2y\right)}\)
\(\dfrac{x-y}{8y^2-2x^2}=\dfrac{-\left(x-y\right)}{2x^2-8y^2}=\dfrac{-\left(x-y\right)}{2\left(x-2y\right)\left(x+2y\right)}\)
\(=\dfrac{-5x\left(x-y\right)}{10x\left(x-2y\right)\left(x+2y\right)}=\dfrac{-5x^2+5xy}{10x\left(x-2y\right)\left(x+2y\right)}\)
KL
4 tháng 8 2017
Đặt A = \(\dfrac{3}{1.6}+\dfrac{3}{6.11}+...+\dfrac{3}{61.66}\)
=> \(\dfrac{5}{3}A=\dfrac{5}{1.6}+\dfrac{5}{6.11}+...+\dfrac{5}{61.66}\)
=> \(\dfrac{5}{3}A=1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{61}-\dfrac{1}{66}\)
=> \(\dfrac{5}{3}A=1-\dfrac{1}{66}=\dfrac{65}{66}\)
=> A = \(\dfrac{13}{22}\)
@nam nguyen
4 tháng 8 2017
Đặt :
\(Â=\dfrac{3}{1.6}+\dfrac{3}{6.11}+...............+\dfrac{3}{61.66}\)
\(\Leftrightarrow A.\dfrac{5}{3}=\dfrac{5}{1.6}+\dfrac{5}{6.11}+..............+\dfrac{5}{61.66}\)
\(\Leftrightarrow A\dfrac{5}{3}=1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+.........+\dfrac{1}{61}-\dfrac{1}{66}\)
\(\Leftrightarrow A.\dfrac{5}{3}=1-\dfrac{1}{66}\)
\(\Leftrightarrow A.\dfrac{5}{3}=\dfrac{65}{66}\)
\(\Leftrightarrow A=\dfrac{13}{22}\)
BM
3
2
28 tháng 5 2022
`(x-3/5)xx3/8-5/8=1/6`
`(x-3/5)xx3/8=1/6+5/8`
`(x-3/5)xx3/8=4/24+15/24=19/24`
`x-3/5=19/24:3/8=19/9`
`x=19/9+3/5=122/45`
_______________________________________________________
`1 1/6-5/6:(x+1/4)=1/2`
`7/6-5/6:(x+1/4)=1/2`
`5/6:(x+1/4)=7/6-1/2=2/3`
`x+1/4=5/6:2/3=5/4`
`x=5/4-1/4=4/4=1`
28 tháng 5 2022
a: \(\left(x-\dfrac{3}{5}\right)\cdot\dfrac{3}{8}-\dfrac{5}{8}=\dfrac{1}{6}\)
\(\Leftrightarrow\left(x-\dfrac{3}{5}\right)\cdot\dfrac{3}{8}=\dfrac{1}{6}+\dfrac{5}{8}=\dfrac{4}{24}+\dfrac{15}{24}=\dfrac{19}{24}\)
\(\Leftrightarrow x-\dfrac{3}{5}=\dfrac{19}{24}:\dfrac{3}{8}=\dfrac{19}{24}\cdot\dfrac{8}{3}=\dfrac{19}{9}\)
hay x=122/45
b: \(\Leftrightarrow\dfrac{7}{6}-\dfrac{5}{6}:\left(x+\dfrac{1}{4}\right)=\dfrac{1}{2}\)
\(\Leftrightarrow\dfrac{5}{6}:\left(x+\dfrac{1}{4}\right)=\dfrac{7}{6}-\dfrac{3}{6}=\dfrac{2}{3}\)
=>x+1/4=5/6:2/3=5/6x3/2=15/12=5/4
=>x=1
1 + 3 + 61 = 65.
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