a: \(\dfrac{x-1}{3}=\dfrac{3}{5}\)
=>\(x-1=3\cdot\dfrac{3}{5}=\dfrac{9}{5}\)
=>\(x=\dfrac{9}{5}+1=\dfrac{14}{5}\)
b: \(\dfrac{2}{x+1}=\dfrac{5}{7}\)(ĐKXĐ: x<>-1)
=>\(x+1=\dfrac{2\cdot7}{5}=2,8\)
=>x=2,8-1=1,8(nhận)
c: \(\left(2+3x\right):\dfrac{-2}{3}=\dfrac{3}{4}:\dfrac{1}{2}\)
=>\(\left(3x+2\right):\dfrac{-2}{3}=\dfrac{3}{4}\cdot2=\dfrac{3}{2}\)
=>\(3x+2=\dfrac{3}{2}\cdot\dfrac{-2}{3}=-1\)
=>3x=-1-3=-3
=>\(x=-\dfrac{3}{3}=-1\)
d:
ĐKXĐ: \(x\ne\dfrac{1}{2}\)
\(\dfrac{-3}{1-2x}=\dfrac{5}{0,75}\)
=>\(\dfrac{3}{2x-1}=\dfrac{20}{3}\)
=>\(2x-1=3\cdot\dfrac{3}{20}=\dfrac{9}{20}=0,45\)
=>2x=1+0,45=1,75
=>\(x=\dfrac{1.75}{2}=0,875\left(nhận\right)\)
e: \(\left(152\dfrac{1}{2}-148\dfrac{3}{8}\right):0,2=x:0,3\)
=>\(x:0,3=\left(152+\dfrac{1}{2}-148-\dfrac{3}{8}\right):0,2\)
=>\(x:0,3=\left(4+\dfrac{4}{8}-\dfrac{3}{8}\right):0,2\)
=>\(x:0,3=\dfrac{33}{8}:\dfrac{1}{5}=\dfrac{165}{8}\)
=>\(x=\dfrac{165}{8}\cdot\dfrac{3}{10}=\dfrac{99}{16}\)
f: \(\left(85\dfrac{7}{30}-83\dfrac{5}{18}\right):2\dfrac{2}{3}=\left(0,01x\right):4\)
=>\(\left(85+\dfrac{7}{30}-83-\dfrac{5}{18}\right):\dfrac{8}{3}=\dfrac{0.01x}{4}\)
=>\(\left(2+\dfrac{21}{90}-\dfrac{25}{90}\right):\dfrac{8}{3}=\dfrac{0.01x}{4}\)
=>\(\left(2-\dfrac{4}{90}\right):\dfrac{8}{3}=\dfrac{0.01x}{4}\)
=>\(\dfrac{11}{15}=\dfrac{0.01x}{4}\)
=>\(0.01x=\dfrac{44}{15}\)
=>\(x=\dfrac{44}{15}:0,01=\dfrac{880}{3}\)
g: \(\left(4-\dfrac{3}{4}\right):\left(2\dfrac{1}{3}-1\dfrac{1}{9}\right)=\left(31x\right):\left(45\dfrac{10}{63}-44\dfrac{25}{84}\right)\)
=>\(\dfrac{13}{4}:\left(2+\dfrac{1}{3}-1-\dfrac{1}{9}\right)=\left(31x\right):\left(45+\dfrac{10}{63}-44-\dfrac{25}{84}\right)\)
=>\(31x:\dfrac{31}{36}=\dfrac{13}{4}:\left(1+\dfrac{2}{9}\right)=\dfrac{13}{4}:\dfrac{11}{9}=\dfrac{117}{44}\)
=>\(36x=\dfrac{117}{44}\)
=>4x=13/44
=>\(x=\dfrac{13}{44}\cdot4=\dfrac{13}{11}\)
h: \(\left[\left(6\dfrac{3}{5}-3\dfrac{3}{14}\right)\cdot2,5\right]:\left(21-1,25\right)=x:5\dfrac{5}{6}\)
=>\(x:\dfrac{35}{6}=\left[\left(6+\dfrac{3}{5}-3-\dfrac{3}{14}\right)\cdot2,5\right]:\left(21-1,25\right)\)
=>\(x:\dfrac{35}{6}=\dfrac{237}{70}\cdot2,5:\dfrac{79}{4}\)
=>\(x:\dfrac{35}{6}=\dfrac{237}{70}\cdot\dfrac{5}{2}\cdot\dfrac{4}{79}\)
=>\(x:\dfrac{35}{6}=\dfrac{3}{7}\)
=>\(x=\dfrac{3}{7}\cdot\dfrac{35}{6}=\dfrac{105}{42}=2,5\)
i: ĐKXĐ: x<>-5
\(\dfrac{x-1}{x+5}=\dfrac{6}{7}\)
=>7*(x-1)=6(x+5)
=>7x-7=6x+30
=>7x-6x=30+7
=>x=37(nhận)
k: \(\dfrac{x^2}{6}=\dfrac{24}{25}\)
=>\(x^2=24\cdot\dfrac{6}{25}=\dfrac{144}{25}\)
=>\(x=\pm\dfrac{12}{5}\)
m: ĐKXĐ: \(x\notin\left\{1;-7\right\}\)
\(\dfrac{x-2}{x-1}=\dfrac{x+4}{x+7}\)
=>\(\left(x-2\right)\left(x+7\right)=\left(x+4\right)\left(x-1\right)\)
=>\(x^2+5x-14=x^2+3x-4\)
=>5x+14=3x-4
=>5x-3x=-4-14
=>2x=-18
=>x=-9(nhận)