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\(\frac{12}{1.4}+\frac{12}{4.7}+\frac{12}{7.10}+...+\frac{12}{97.100}\)
\(=\frac{12}{3}.\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{97.100}\right)\)
\(=4.\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{97}-\frac{1}{100}\right)\)
\(=4.\left(1-\frac{1}{100}\right)=4.\frac{99}{100}=\frac{99}{25}\)
2x-\(\frac{1}{3}\)=1-\(\frac{5}{6}\)
2x-\(\frac{1}{3}\)=\(\frac{1}{6}\)
2x=\(\frac{1}{6}\)+\(\frac{1}{3}\)
2x=1/6 +2/6
2x=\(\frac{1}{2}\)
x=1/2 : 2
x/\(\frac{1}{4}\)
\(\frac{7}{9}\):(2+\(\frac{3}{4}\)x)+\(\frac{5}{9}\)=\(\frac{23}{27}\)
7/9 :(2+3/4x)=\(\frac{23}{27}\)-\(\frac{5}{9}\)
7/9 :(2+3/4x)=\(\frac{23}{27}\)-\(\frac{15}{27}\)
7/9 :(2+3/4x)=\(\frac{8}{27}\)
(2+3/4x) =\(\frac{7}{9}\) . \(\frac{27}{8}\)
(2+3/4x) =\(\frac{21}{8}\)
\(\frac{3}{4}\)x =\(\frac{21}{8}\)-2
3/4x =21/8 -16/8
3/4x = 5/8
x =\(\frac{5}{8}\) : \(\frac{3}{4}\)
x =5/8 . 4/3
x =\(\frac{20}{24}\)
\(\frac{\frac{1}{4}+\frac{1}{24}+\frac{1}{124}}{\frac{3}{4}+\frac{3}{24}+\frac{3}{124}}\) + \(\frac{\frac{2}{7}+\frac{2}{17}+\frac{2}{127}}{\frac{3}{7}+\frac{3}{17}+\frac{3}{127}}\)
= \(\frac{\frac{1}{4}+\frac{1}{24}+\frac{1}{124}}{3.\left(\frac{1}{4}+\frac{1}{24}+\frac{1}{124}\right)}\) + \(\frac{2.\left(\frac{1}{7}+\frac{1}{17}+\frac{1}{127}\right)}{3.\left(\frac{1}{7}+\frac{1}{17}+\frac{1}{127}\right)}\)
= \(\frac{1}{3}\) + \(\frac{2}{3}\) = 1
A=-1/2*-2/3*-3/4*..*-2013/2014
A=-1*-2*-3*...*-2013/2*3*4*...*2014
A=-1/2014
ta có(-1)^2015=-1
B=-1/2015>-1/2014=A
nên A<B
\(\frac{x-4}{y-3}=\frac{4}{3}\Rightarrow\frac{x-4}{4}=\frac{y-3}{3}\)
Áp dụng TC của DTSBN ta có:
\(\frac{x-4}{4}=\frac{y-3}{3}=\frac{x-4-y+3}{4-3}=\frac{5-1}{1}=4\)
Suy ra: (x-4)/4=4 =>x-4=16=>x=20
(y-3)/3=4=>y-3=12=>x=15
x-4/y-3=4/3
=>3.(x-4)=4.(y-3)
=>3x-12=4y-12
=>3x=4y
Mà x-y=5=>x=y+5
=>3.(y+5)=4y
=>3y+15=4y=>4y-3y=15=>y=15
Khi đó x=15+5=20
Vậy x=20;y=15
cho mình hỏi cách tính dc ko bn
có thể ghi cách tính ra luôn
\(\frac{x+1}{97}+\frac{x+1}{98}=\frac{x+1}{99}+\frac{x+1}{100}\)
\(=>\frac{x+1}{97}+\frac{x+1}{98}-\frac{x+1}{99}-\frac{x+1}{100}=0\)
\(=>\left(x+1\right).\left(\frac{1}{97}+\frac{1}{98}-\frac{1}{99}-\frac{1}{100}\right)=0\)
Vì \(\frac{1}{97}>\frac{1}{98}>\frac{1}{99}>\frac{1}{100}\)
Nên \(\frac{1}{97}+\frac{1}{98}-\frac{1}{99}-\frac{1}{100}\) khác 0
=>x+1=0
=>x=-1
Vậy x=-1
* 1/2 + x = 5/6 => x =5/6 - 1/2 = 2/6 = 1/3
*x + 1/4 =3/4 => x = 3/4 - 1/4 =2/4= 1/2
*5/6 - x = 1/3 => x = 5/6 -1/3 = 3/6 = 1/2
*3/10 + x = 1/2 => x = 1/2 -3/10 = 2/10 = 1/5