Mianownik musi być różny od zera (nie dzielimy przez zero).
a)
[tex]\frac{2}{x-3} = 4\\\\x-3 \neq 0\\\\x \neq 3\\\\\boxed{D= R\setminus\{3\}}[/tex]
[tex]4(x-3) = 2 \ \ \ |:2\\\\2(x-3) = 1\\\\2x-6 = 1\\\\2x = 1+6\\\\2x = 7 \ \ \ |:2\\\\\underline{x = 3\frac{1}{2}}[/tex]
b)
[tex]\frac{x-1}{x+2} = 3\\\\x+2 \neq 0\\\\x \neq -2\\\\\boxed{D = R \setminus\{-2\}}[/tex]
[tex]3(x+2) = x-1\\\\3x+6 = x-1\\\\3x-x = -1-6\\\\2x = -7 \ \ \ |:2\\\\\underline{x = -3\frac{1}{2}}[/tex]
c)
[tex]\frac{4x}{x-5} = -2\\\\x-5 \neq 0\\\\x \neq 5\\\\\boxed{D = R\setminus\{5\}}[/tex]
[tex]-2(x-5) = 4x \ \ \ |:(-2)\\\\x-5 = -2x\\\\x+2x = 5\\\\3x = 5 \ \ \ |:3\\\\\underline{x = 1\frac{2}{3}}[/tex]
