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a, \(\frac{x-6}{x+4}=\frac{2}{7}\Rightarrow7x-42=2x+8\)ĐK : \(x\ne-4\)
\(\Leftrightarrow5x=50\Leftrightarrow x=10\)(tm)
b, \(\left(x+5\right):2\frac{1}{2}=\frac{40}{x+5}\)ĐK : \(x\ne-5\)
\(\Leftrightarrow\frac{5\left(x+5\right)}{2}=\frac{40}{x+5}\Rightarrow5\left(x+5\right)^2=80\Leftrightarrow\left(x+5\right)^2=16\)
TH1 : \(x+5=4\Leftrightarrow x=-1\)
TH2 : \(x+5=-4\Leftrightarrow x=-9\)
a) - 0,52 : x = - 9,36 : 16,38
- 0,52 : x = \(-\frac{4}{7}\)
\(x=\left(-0,52\right):\left(-\frac{4}{7}\right)=\frac{91}{100}=0,91\)
b) \(\frac{4\frac{1}{4}}{2\frac{7}{8}}=\frac{x}{1,61}\)
\(\frac{\frac{17}{4}}{\frac{23}{8}}=\frac{x}{1,61}\)
\(\frac{x}{1,61}=\frac{34}{23}\)
\(x=\frac{34}{23}.1,61=2,38\)
\(\frac{4\frac{1}{4}}{2\frac{7}{8}}=\frac{x}{1,61}\)
\(\Leftrightarrow\frac{\frac{17}{4}}{\frac{23}{8}}=\frac{x}{1,61}\)
\(\Leftrightarrow\frac{34}{23}=\frac{x}{1,61}\)
\(\Leftrightarrow x=\frac{34}{23}.1,61\)
\(\Leftrightarrow x=\frac{119}{50}\)
\(\frac{x-1}{x-2}=\frac{x+3}{x+4}\)
\(\Rightarrow\left(x-1\right)\left(x+4\right)=\left(x-2\right)\left(x+3\right)\)
\(\Leftrightarrow x^2+4x-x-4=x^2+3x-2x-6\)
\(\Leftrightarrow x^2+4x-x-4-x^2-3x+2x+6=0\)
\(\Leftrightarrow2x+2=0\)
\(\Leftrightarrow2x=-2\)
\(\Leftrightarrow x=-1\)VẬY X=-1 LÀ NGHIỆM CỦA PHƯƠNG TRÌNH \(\frac{x-1}{x-2}=\frac{x+3}{x+4}\)
\(\text{a)}\frac{37-x}{x+13}=\frac{3}{7}\)
\(\Leftrightarrow3\left(x+13\right)=7\left(37-x\right)\)
\(\Leftrightarrow3x+39=259-7x\)
\(\Leftrightarrow3x+7x=259-39\)
\(\Leftrightarrow10x=220\)
\(\Leftrightarrow x=22\)
\(\text{b)}\frac{x+4}{20}=\frac{5}{x+4}\)
\(\Leftrightarrow\left(x+4\right)^2=100\)
\(\Leftrightarrow\orbr{\begin{cases}x+4=10\\x+4=-10\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=6\\x=-14\end{cases}}\)
Bài 2:
a: =>x/4=1/8
hay x=1/2
b: \(\Leftrightarrow\dfrac{x}{-5}=\dfrac{11}{6}\)
hay x=-55/6
c: \(\Leftrightarrow\dfrac{-3.5}{x}=\dfrac{4.25}{8}\)
hay x=-112/17
a) \(\frac{x}{7}=\frac{18}{14}\)
\(\frac{x}{7}=\frac{9}{7}\)
\(\Rightarrow x=9\)
b) \(6:x=1\frac{3}{4}:5\)
\(6:x=\frac{7}{4}.\frac{1}{5}\)
\(6:x=\frac{7}{20}\)
\(x=6:\frac{7}{20}\)
\(x=\frac{120}{7}\)
vay \(x=\frac{120}{7}\)
c) \(\frac{5,7}{0,35}=\frac{-x}{0,45}\)
\(\Rightarrow-0,35x=5,7.0,45\)
\(\Rightarrow-0,35x=2,565\)
\(\Rightarrow x=\frac{-2,565}{0,35}\)
\(\Rightarrow x=\frac{-513}{70}\)
vay \(x=\frac{-513}{70}\)
a)\(\frac{x-1}{x+2}=\frac{x-2}{x+3}\Rightarrow\left(x-1\right)\left(x+3\right)=\left(x+2\right)\left(x-2\right)\)
\(\Rightarrow x^2+2x-3=x^2-4\)
\(\Rightarrow2x=-1\)
\(\Rightarrow x=-\frac{1}{2}\)
b)\(\frac{37-x}{x+13}=\frac{3}{7}\)\(\Rightarrow7\left(37-x\right)=3\left(x+13\right)\)
\(\Rightarrow259-7x=3x+39\)
\(\Rightarrow10x=220\)
\(\Rightarrow x=22\)
a) \(\frac{x}{27}=\frac{-2}{3,6}\Leftrightarrow x=\frac{-2.27}{3,6}=-15\)
b) \(\frac{4\frac{1}{4}}{2\frac{7}{8}}=\frac{x}{1,61}\Leftrightarrow\frac{4,25}{2,875}=\frac{x}{1,61}\Leftrightarrow x=\frac{4,25.1,61}{2,875}=2,38\)
a) \(\frac{x}{27}=-\frac{2}{3,6}\Rightarrow x=\frac{-2.27}{3,6}=-15\)
b) \(\frac{4\frac{1}{4}}{2\frac{7}{8}}=\frac{x}{1,61}\Rightarrow\frac{\frac{17}{4}}{\frac{23}{8}}=\frac{x}{1,61}\Leftrightarrow\frac{17}{4}\cdot\frac{8}{23}=\frac{x}{1,61}\)
\(\frac{34}{23}=\frac{x}{1,61}\Rightarrow x=\frac{1,61.34}{23}=2,38\)
