7.(x-1)= 5.(x+5)

7.x-7. = 5.x+25

7.x -5.x =25+7

2.x.    = 32

         x  = 32:2

       x.    = 16

làm rõ ràng, đầy đủ chi tiết luôn

$\frac{x-1}{x+5}=\frac{5}{7}$

=>(x-1).7=(x+5).5

=>7x-7=5x+25

=>2x=32

=>x=16

lộn na !!

7x - 7 - 5x - 35 = 0

2x + 28 = 0

2x = -28

x = -14 

a) \(\frac{x-1}{x+5}=\frac{6}{7}\)

7( x - 1 ) = 6( x + 5 )

7x - 7 = 6x - 30

7x - 6x = -30 + 7

x = -23

b) \(\frac{x^2}{6}=\frac{24}{25}\)

\(x^2.25=6.24\)

\(x^2.25=144\)

\(x^2=\frac{144}{25}\)

\(x=\sqrt{\frac{144}{25}}\)

\(x=\frac{12}{5}\)

c) \(\frac{x-2}{x-4}=\frac{x+4}{x+7}\)

\(\left(x-2\right)\left(x+7\right)=\left(x+4\right)\left(x-4\right)\)

\(x^2+7x-2x-14=x^2-4x+4x-16\)

\(x^2+5x-14=x^2^{ }-16\)

\(x^2-x^2+5x=-16+14\)

\(5x=-2\)\(x=\frac{-2}{5}\)

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) \(\frac{x-1}{x+5}=\frac{6}{7}\)

\(\Rightarrow7.\left(x-1\right)=6.\left(x+5\right)\)

\(\Rightarrow7x-7=6x+30\)

\(\Rightarrow7x-6x=7+30\)

\(\Rightarrow x=37\)

b) \(\frac{x^2}{6}=\frac{24}{25}\)

\(\Rightarrow25.x^2=24.6\)

\(\Rightarrow25.x^2=144\)

\(\Rightarrow x^2=144:25\)

\(\Rightarrow x^2=\frac{144}{25}\)

\(\Rightarrow x^2=\frac{12^2}{5^2}\)

\(\Rightarrow x^2=\frac{12}{5}^2\)

\(\Rightarrow x=\pm\frac{12}{5}\)

\(c,\frac{x-2}{x-1}=\frac{x+4}{x+7}\)

\(\Leftrightarrow(x-2)(x+7)=(x+4)(x-1)\)

\(\Leftrightarrow x^2+5x-14=x^2+3x-4\)

\(\Leftrightarrow x^2+5x-14-x^2+3x=-4\)

\(\Leftrightarrow\left[x^2-x^2\right]+5x-3x-14=-4\)

\(\Leftrightarrow2x-14=-4\)

\(\Leftrightarrow2x=10\Leftrightarrow x=5\)

\(\frac{x-3}{5-x}=\frac{5}{7}\)

\(\Leftrightarrow\left(x-3\right).7=5.\left(5-x\right)\)

\(\Leftrightarrow7x-21=25-5x\)

\(\Leftrightarrow7x+5x=25+21\)

\(\Leftrightarrow12x=46\)

\(\Leftrightarrow x=\frac{46}{12}=\frac{23}{6}\)

Vậy x = \(\frac{23}{6}\)

7x-21=25-5x

12x=46

x=23/6

\(\Leftrightarrow\left(x-2\right)\left(x+7\right)=\left(x-1\right)\left(x+4\right)\Leftrightarrow x^2+5x-14=x^2+3x-4\Leftrightarrow2x=10\Leftrightarrow x=5\)

x² ở đâu có vạy bạn 

\(\frac{x-2}{x-1}=\frac{x+4}{x+7}\)

\(\Leftrightarrow\left(x-2\right)\left(x+7\right)=\left(x-1\right)\left(x+4\right)\)

\(\Leftrightarrow x^2+5x-14=x^2+3x-4\)

\(\Leftrightarrow x^2+15=x^2+3x-4+14\)

\(\Leftrightarrow x^2+15=x^2+3x+10\)

\(\Leftrightarrow x^2+5x-\left(x^2+3x\right)=x^2+3x+10-\left(x^2+3x\right)\)

\(\Leftrightarrow2x=10\)

=> x = 5

a) \(\frac{3x-2}{1\frac{2}{5}}=\frac{2\frac{3}{7}}{2\frac{3}{5}}\Rightarrow3x-2=1.\frac{2}{5}.\frac{2\frac{3}{7}}{2\frac{3}{5}}=\frac{7}{5}.\frac{17}{7}.\frac{5}{13}\)

\(3x-2=\frac{17}{13}\Rightarrow3x=2+\frac{17}{13}=\frac{43}{13}\Rightarrow x=\frac{43}{39}.\)

b) \(\frac{x}{0,16}=\frac{9}{x}\Rightarrow x^2=9.0,16=1,44\Rightarrow x=\pm1,2\)