[tex]a) \ \frac{9x^{2}-1}{x^{2}+x}\cdot\frac{(x+1)^{2}}{(x+1)(3x-1)} = \frac{(3x-1)(3x+1)}{x(x+1)}\cdot\frac{(x+1)^{2}}{(x+1)(3x-1)} =\boxed{ \frac{3x+1}{x}}\\\\\\Zal:\\x+1 \neq 0 \ \ i \ \ x\neq 0 \ \ i \ \ 3x-1 \neq 0\\\\x\neq -1 \ \ i \ x\neq 0 \ \ i \ \ x\neq \frac{1}{3}[/tex]
[tex]b) \ \frac{(x-3)(x+2)}x^{2}}:\frac{(x^{2}-9)(x+1)}{(x^{2}+x)(x^{2}+3x)} = \frac{(x-1)(x+2)}{x^{2}}\cdot\frac{(x^{2}+x)(x^{2}+3x)}{(x^{2}-9)(x+1)} =\frac{(x-3)(x+2)}{x^{2}}\cdot\frac{x(x+1)\cdot x(x+3)}{(x-3)(x+3)(x+1)}=\\\\=\frac{x^{2}(x+2)}{x^{2}}}=\boxed{x+2}\\\\\\Zal:\\x+3 \neq 0 \ \ i \ \ x+1\neq 0 \ \ i \ \ x^{2}\neq 0 \ \ i \ \ x-1\neq 0\\\\x\neq -3 \ \ i \ \ x\neq -1 \ \ i \ \ x\neq 0 \ \ i \ \ x \neq 1[/tex]
