a)
[tex]\frac{x}{x-1} = \frac{x+2}{x} \ \ \ |\cdot x(x-1)\\\\\\Zal:\\x \neq 0\\i\\x-1\neq 0 \ \ \rightarrow \ \ x\neq 1\\D = R\setminus\{0,1\}[/tex]
[tex](x+2)(x-1) = x^{2}\\\\x^{2}-x+2x-2 = x^{2}\\\\x -2 = 0\\\\\boxed{x = 2}[/tex]
b)
[tex]\frac{4x+7}{x+1} = x+3 \ \ \ |\cdot (x+1)\\\\\\Zal:\\x+1 \neq 0 \ \ \rightarrow \ \ x \neq -1\\D = R\setminus\{-1\}[/tex]
[tex](x+3)(x+1) = 4x+7\\\\x^{2}+x+3x+3 = 4x+7\\\\x^{2}+4x-4x+3-7 =0\\\\x^{2}-4 = 0\\\\x^{2}-2^{2} = 0[/tex]
(a + b)(a - b) = a² - b²
[tex](x+2)(x-2) = 0\\\\x+2 = 0 \ \vee \ x-2 = 0\\\\x = -2 \ \vee \ x = 2\\\\\boxed{x\in\{-2,2\}}[/tex]
