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1.\(\frac{x+1}{x-2}=\frac{3}{4}\)
\(\Leftrightarrow\left(x+1\right).4=\left(x-2\right).3\)
\(\Leftrightarrow4x+4=3x-6\)
<=>4x-3x=-6-4
<=>x=-10
2.\(\frac{52}{2x-1}=\frac{13}{30}\)
<=>52.30=(2x-1).13
<=>1560=26x-13
<=>-26x=-13-1560
<=>-26x=-1573
<=>x=60,5
3.\(\frac{2x-3}{x+1}=\frac{4}{7}\)
<=>(2x-3).7=(x+1).4
<=>14x-21=4x+4
<=>14x-4x=4+21
<=>10x=25
<=>x=2,5
4.\(\frac{2x+3}{42}=\frac{3x-1}{32}\)
<=>(2x+3).32=42(3x-1)
<=>64x+96=126x-42
<=>64x-126x=-42-96
<=>-62x=-138
<=>x=69/31
a. 2x-1+ 5.2x-1:2=7/32
=> 2x+1.(1+5/2)=7/32
=>2x+1.7/2=7/32
=> 2x+1=1/16=1/24
=> x+1=-4=>x=-5
\(2^{x-1}+5.2^{x-2}=\frac{7}{32}\)
\(\Rightarrow2^{x-1}+5.2^{x-1}.2^3=\frac{7}{32}\)
\(\Rightarrow2^{x-1}.\left(1+5.2^3\right)=\frac{7}{32}\)
\(\Rightarrow2^{x-1}.41=\frac{7}{32}\)
\(\Rightarrow2^{x-1}=\frac{7}{1312}\)
\(\Rightarrow\) Ko có x thỏa mãn
\(2^{x-1}+5.2^{x-2}=\frac{7}{32}\)
\(\Rightarrow2^{x-1}+2^{x-1}.\frac{5}{2}=\frac{7}{32}\Rightarrow2^{x-1}.\left(1+\frac{5}{2}\right)=\frac{7}{32}\Rightarrow2^{x-1}.\frac{7}{2}=\frac{7}{32}\)
\(\Rightarrow2^{x-1}=\frac{7}{32}:\frac{7}{2}=\frac{7}{32}.\frac{2}{7}=\frac{1}{16}\)
\(\Rightarrow2^{x-1}=2^{-4}\Rightarrow x-1=-4\Rightarrow x=-4+1=-3\)