[tex]2a)\\\\\frac{2}{x}=\frac{3}{x-1}\\\\x\neq 0\ \ \wedge \ \ x-1\neq 0\\\\x\neq 0\ \ \wedge \ \ x \neq 1\\\\D=R\setminus \left \{ 0,1 \right \}\\\\3x=2(x-1) \\\\3x=2x-2\\\\3x-2x=-2\\\\x=-2[/tex]
[tex]b)\\\\\frac{4}{x+1}=\frac{5}{x }\\\\x\neq 0\ \ \wedge \ \ x+1\neq 0\\\\x\neq 0\ \ \wedge \ \ x \neq -1\\\\D=R\setminus \left \{ -1,0\right \}\\\\ 5(x+1)=4x \\\\5x+54x\\\\5x-4x=-5\\\\x=-5[/tex]
[tex]c)\\\\\frac{3}{5}=\frac{2x-1}{2-5x} \\\\ 2-5x\neq 0\\\\-5x\neq -2 \ \ |:(-5)\\\\x\neq \frac{2}{5}\\\\D=R\setminus \left \{ \frac{2}{5}\right \}[/tex]
[tex]5(2x-1)=3(2-5x)\\\\10x-5=6-15x\\\\10x+15x=6+5\\\\25x=11\ \ |:25\\\\x=\frac{11}{25}[/tex]
[tex]d)\\\\\frac{2x+1}{1-2x}=\frac{2}{3} \\\\1-2x\neq 0\\\\-2x\neq -1 \ \ |:(-2)\\\\x\neq \frac{1}{2}\\\\D=R\setminus \left \{ \frac{1}{2}\right \}[/tex]
[tex]3(2x+1)=2(1-2x)\\\\ 6x+3=2-4x\\\\6x+4x=2-3\\\\10x=-1\ \ |:10\\\\x=-\frac{1}{10}[/tex]
[tex]e)\\\\\frac{0,4x-1}{3}=\frac{2x-5}{2} \\\\ 3(2x-5)=2(0,4x-1)\\\\6x-15=0,8x-2\\\\6x-0,8x=-2+15\\\\5,2x=13\ \ |*10\\\\52x=130\ \ |:52\\\\x=\frac{130}{52}=\frac{5}{2}=2\frac{1}{2}[/tex]
[tex]f)\\\\\frac{4+x^2}{x}=\frac{2x-1}{2} \\\\ x\neq 0 \\\\D=R\setminus \left \{ 0\right \}[/tex]
[tex]2( 4+x^2)=x (2x-1) \\\\8+2x^2=2x^2-x\\\\2x^2-2x^2+x=-8\\\\x=-8[/tex]
