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a) \(\frac{2}{7}x-\frac{1}{3}x=\frac{5}{21}\)
\(\left(\frac{2}{7}-\frac{1}{3}\right)x=\frac{5}{21}\)
\(\left(-\frac{1}{21}\right)x=\frac{5}{21}\Rightarrow x=\frac{5}{21}:-\frac{1}{21}=-5\)
b) \(\frac{x+1}{1974}+\frac{x+2}{1973}+\frac{x+3}{1972}=-3\)
\(\left(\frac{x+1}{1974}+1\right)+\left(\frac{x+2}{1973}+1\right)+\left(\frac{x+3}{1972}+1\right)=-3+3\)
\(\frac{x+1975}{1974}+\frac{x+1975}{1973}+\frac{x+1975}{1972}=0\)
\(\left(x+1975\right)\left(\frac{1}{1974}+\frac{1}{1973}+\frac{1}{1972}\right)=0\)
Mà \(\frac{1}{1974}+\frac{1}{1973}+\frac{1}{1972}>0\Rightarrow x+1975=0\)
\(x=-1975\)
\(\frac{x+1}{1974}+1+\frac{x+2}{1973}+1+\frac{x+3}{1972}+1=-3+3\)
\(\Leftrightarrow\frac{x+1975}{1974}+\frac{x+1975}{1973}+\frac{x+1975}{1972}=0\)
\(\Leftrightarrow\left(x+1975\right)\left(\frac{1}{1974}+\frac{1}{1973}+\frac{1}{1972}\right)=0\)
=> x + 1975 = 0. => x = -1975 ( vì 1/1974 + 1/1973 + 1/1972 khác 0 )
\(\frac{x+1}{1974}+\frac{x+2}{1973}+\frac{x+3}{1972}=-3\)
\(\Rightarrow\left(\frac{x+1}{1974}+1\right)+\left(\frac{x+2}{1973}+1\right)+\left(\frac{x+3}{1972}+1\right)=0\)
\(\Rightarrow\frac{x+1+1974}{1974}+\frac{x+2+1973}{1973}+\frac{x+3+1972}{1972}=0\)
\(\Rightarrow\frac{x+1975}{1974}+\frac{x+1975}{1973}+\frac{x+1975}{1972}=0\)
\(\Rightarrow\left(x+1975\right)\frac{1}{1974}+\frac{1}{1973}+\frac{1}{1972}=0\)
Mà \(\frac{1}{1974}+\frac{1}{1973}+\frac{1}{1972}\ne0\)
\(\Rightarrow x+1975=0\)
\(\Rightarrow x=0+1975\)
\(\Rightarrow x=1975\)
Vậy \(x=1975\)
b) phần này làm tương tự phần a nha, chuyển -3 sang vế bên trái r cộng từng p.số vs 1 và sau đó nhóm tử số chung ra ngoài ^^
\(\frac{x+1}{1974}+\frac{x+2}{1973}+\frac{x+3}{1972}=-3\)
\(=>\left(\frac{x+1}{1974}+1\right)+\left(\frac{x+2}{1973}+1\right)+\left(\frac{x+3}{1972}+1\right)=-3+3\)
\(=>\frac{x+1975}{1974}+\frac{x+1975}{1973}+\frac{x+1975}{1972}=0\)
\(\left(x+1975\right)\left(\frac{1}{1974}+\frac{1}{1973}+\frac{1}{1972}\right)=0\)
\(=>x+1975=0=>x=-1975\)
Vậy \(x=-1975\)
\(\frac{x+1}{1974}+\frac{x+2}{1973}+\frac{x+3}{1972}=-3\)
\(\Leftrightarrow\left(\frac{x+1}{1974}+1\right)+\left(\frac{x+2}{1973}+1\right)+\left(\frac{x+3}{1972}+1\right)=0\)
\(\Leftrightarrow\frac{x+1975}{1974}+\frac{x+1975}{1973}+\frac{x+1975}{1972}=0\)
\(\Leftrightarrow\left(x+1975\right)\left(\frac{1}{1974}+\frac{1}{1973}+\frac{1}{1972}\right)=0\)
\(\Leftrightarrow x+1975=0\)
\(\Leftrightarrow x=-1975\)
\(\frac{2}{3}x+\frac{5}{7}=\frac{3}{10}\)
\(\Rightarrow\frac{2}{3}x=\frac{3}{10}-\frac{5}{7}\)
\(\Rightarrow\frac{2}{3}x=-\frac{29}{70}\)
\(\Rightarrow x=-\frac{29}{70}:\frac{2}{3}\)
\(\Rightarrow x=-\frac{87}{140}\)
tíc mình nha
a) \(\frac{x-3}{x+5}=\frac{5}{7}\)
\(\Rightarrow\left(x-3\right).7=\left(x+5\right).5\)
\(\Rightarrow7x-21=5x+25\)
\(\Rightarrow7x-5x=21+25\)
\(\Rightarrow2x=46\)
\(\Rightarrow x=23\)
Vậy \(x=23\)
b) \(\frac{7}{x-1}=\frac{x+1}{9}\)
\(\Rightarrow\left(x-1\right).\left(x+1\right)=7.9\)
\(\Rightarrow\left(x-1\right)x-\left(x+1\right)=7.9\)
\(\Rightarrow x^2-x-x-1=63\)
\(\Rightarrow x^2-1=63\)
\(\Rightarrow x^2=64\)
\(\Rightarrow x=8\) hoặc \(x=-8\)
Vậy \(x=8\) hoặc \(x=-8\)
c) \(\frac{x+4}{20}=\frac{5}{x+4}\)
\(\Rightarrow\left(x+4\right)^2=100\)
\(\Rightarrow x+4=\pm10\)
+) \(x+4=10\Rightarrow x=6\)
+) \(x+4=-10\Rightarrow x=-16\)
Vậy \(x\in\left\{6;-16\right\}\)
sai đề
\(\frac{x+1}{1974}+\frac{x+2}{1973}+\frac{x+3}{1972}=3\)
x+1/1974+1+x+2/1973+1+x+3/1972=0
x+1+1974/1974+x+2+1973/1973+x+3+1972/1972=0
x+1975/1974+x+1975/1973+x+1975/1972=0
(x+1975)(1/1974+1/1973+1/1972)=0
=>x+1975=0 vì 1/1974+1/1973+1/1972 Khác 0
=>x=-1975