X-1/x+2=x-2/x+3

=>(x-1)(x+3)=(x+2)(x-2)

=>x(x+3)-1(x+3)=x(x-2)+2(x-2)

=>x^2+3x-x-3=x^2-2x+2x-4

=>x^2+2x-3=x^2-4

=>2x-3=-4=>x=-1/2=-0,5

 vậy...

\(\frac{x-1}{x+2}=\frac{x-2}{x+3}\Leftrightarrow\left(x-1\right)\left(x+3\right)=\left(x-2\right)\left(x+2\right)\)

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

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

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

                      \(\Leftrightarrow2x=-1\Leftrightarrow x=-\frac{1}{2}\)

\(\frac{7x+2}{5x+7}=\frac{7x-1}{5x+1}=\frac{7x+2-7x+1}{5x+7-5x-1}=\frac{3}{6}=\frac{1}{2}\)

\(2\left(7x+2\right)=5x+7\)

\(14x-5x=7-4\)

\(9x=3\)

\(\Rightarrow x=3\div9\)

\(\Rightarrow x=\frac{1}{3}\)

nhân chéo ta được:

\(\left(7x+2\right)\left(5x+1\right)=\left(5x+7\right)\left(7x-1\right)\)

\(35x^2+7x+10x+2=35x^2-5x+49x-7\) ( nhân phân phối)

\(35x^2-35x^2+7x+10x-5x+49x=-2-7\)

\(-27x=-9\)

\(x=\frac{-9}{-27}\)

\(x=\frac{1}{3}\)

=>x=1/3

Áp dụng tính chất của dãy tỉ số bằng nhau ta có:

\(\frac{7x+2}{5x+7}=\frac{7x-1}{5x+1}=\frac{\left(7x+2\right)-\left(7x-1\right)}{\left(5x+7\right)-\left(5x+1\right)}=\frac{3}{6}=\frac{1}{2}\)

=> 2(7x + 2) = 5x + 7

14x + 4 = 5x + 7

14x - 5x = 7 - 4

9x = 3

x = 3:9

x = 0,(3)