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\(71+52,5\times4=\frac{x+140}{x}+210\)
\(71+210=\frac{x+140}{x}+210\)
\(=>\frac{x+140}{x}=71\)
\(71=\frac{142}{2}\)\(\Rightarrow x=142-140=2\)
<=> 71=\(\dfrac{x+140}{x}\)
=>71x=x+140
<=>71x-x=140
<=>70x=140
<=>x=2
Vậy x=2
=13/12x14/13x15/14x16/15x...x2006/2005x2007/2006x2008/2007
=2008/12
=502/3
A = 1\(\dfrac{1}{12}\) \(\times\) 1\(\dfrac{1}{13}\) \(\times\) 1\(\dfrac{1}{14}\) \(\times\) 1\(\dfrac{1}{15}\) \(\times\) ... \(\times\) 1\(\dfrac{1}{2005}\) \(\times\) 1\(\dfrac{1}{2006}\) \(\times\) 1\(\dfrac{1}{2007}\)
A = ( 1 + \(\dfrac{1}{12}\)) \(\times\) ( 1 + \(\dfrac{1}{13}\)) \(\times\) ( 1 + \(\dfrac{1}{14}\)) \(\times\)...\(\times\) ( 1 + \(\dfrac{1}{2006}\))\(\times\)(1+\(\dfrac{1}{2007}\))
A = \(\dfrac{13}{12}\) \(\times\) \(\dfrac{14}{13}\) \(\times\) \(\dfrac{15}{14}\) \(\times\) ...\(\times\) \(\dfrac{2007}{2006}\) \(\times\) \(\dfrac{2008}{2007}\)
A = \(\dfrac{13\times14\times15\times...\times2007}{13\times14\times15\times...\times2007}\) \(\times\) \(\dfrac{2008}{12}\)
A = 1 \(\times\) \(\dfrac{502}{3}\)
A = \(\dfrac{502}{3}\)
(x + 20) : 99 = (1004 + 1) x 2/99
=> 99x + 1980 = 1005 x 2/99
=> 99x = 99495/2 - 1980
=> 99x = 95535/2
=> x = 965/2
b. \(\frac{x+140}{x}\) + 260 = 21 + 65 x 4
=> \(\frac{x+140}{x}\)= 21 + 260 - 260
=> \(\frac{x+140}{x}\)= 21
=> 21x = x + 140
=> 20x = 140
=> x = 7
Ta có công thức tổng quát:
\(\dfrac{k}{n\cdot\left(n+k\right)}=\dfrac{1}{n}-\dfrac{1}{n+k}\)
\(a,A=\dfrac{1}{5\cdot8}+\dfrac{1}{8\cdot11}+...+\dfrac{1}{x\left(x+3\right)}\\ =\dfrac{1}{3}\left(\dfrac{3}{5\cdot8}+\dfrac{3}{8\cdot11}+...+\dfrac{3}{x\left(x+3\right)}\right)\\ =\dfrac{1}{3}\left(\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{x}-\dfrac{1}{x+3}\right)\\ =\dfrac{1}{3}\cdot\left(\dfrac{1}{5}-\dfrac{1}{x+3}\right)\\ =\dfrac{1}{3}\cdot\dfrac{x-2}{5\left(x+3\right)}\\ =\dfrac{x-2}{15\left(x+3\right)}\)
Theo đề bài ta có:
\(A=\dfrac{101}{1540}\\ \Rightarrow\dfrac{x-2}{15\left(x+3\right)}=\dfrac{101}{1540}\\ \Rightarrow\dfrac{x-2}{x+3}=\dfrac{303}{308}\\ \Rightarrow\dfrac{x-2}{x+3}=\dfrac{305-2}{305+3}\\ \Rightarrow x=305\)
\(a,\)\(71+65\times4=\frac{x+140}{x}+260\)
\(\Rightarrow71+260=\frac{x-140}{x}+260\)
\(\Rightarrow71=\frac{x-140}{x}\)
\(\Rightarrow71x=x-140\)
\(\Rightarrow71x-x=-140\)
\(\Rightarrow70x=-140\)
\(\Rightarrow x=-2\)
\(b,\)\(y\times\frac{15}{2}-\frac{1}{3}\times\left(\frac{1}{4}+y\right)=90\frac{2}{3}\)
\(\Rightarrow\frac{15y}{2}-\frac{1}{12}-\frac{y}{3}=\frac{272}{3}\)
\(\Rightarrow\frac{90y}{12}-\frac{1}{12}-\frac{4y}{12}=\frac{1088}{12}\)
\(\Rightarrow90y-1-4y=1088\)
\(\Rightarrow86y=1089\)
\(\Rightarrow y=\frac{1089}{86}\)
\(71+65\cdot4=\frac{x+140}{x}+260\)
\(\Rightarrow71+260=\frac{x}{x}+\frac{140}{x}+260\)
\(\Rightarrow71=1+\frac{140}{x}\)
\(\Rightarrow\frac{140}{x}=70\)
\(\Rightarrow x=2\)
71+65*4=x+140 +260
x
=>71+260= x + 140 +260
x x
=>71=1+ 140
x
=> 71-1 = 140
x
=> 70=140:x
=>x=140:70=2
\(\frac{x+140}{x}+260=21+65×4\)
\(\frac{x+140}{x}+260=21+260\)
\(\frac{x+140}{x}=21\)
\(\left(x+140\right):x=21\)
x + 140=21× x
140= 21× X - X
140= 21×X-X×1
140=(21-1)×X
140=20×X
X=140:20
X=7
địt mẹ cái thằng ngu hốc cặc
\(\dfrac{x+140}{x}\) = 70 x 2 + 1
\(x\) + 140 = (140 + 1) x \(x\)
\(x\) + 140 = 141 x \(x\)
\(141\) x \(x\) - \(x\) = 140
\(x\) x (141 - 1) = 140
\(x\) x 140 =140
\(x\) = 140 : 140
\(x\) = 1