Odpowiedź:
[tex]\displaystyle \frac{x}{x+2}- \frac{3x+1}{3x} =\frac{3x^2-(3x+1)(x+2)}{3x(x+2)} =\frac{3x^{2} -3x^{2} -7x-2}{3x(x+1)} =\\\frac{-7x-2}{3x(x+1)} \qquad D=R-\{-1,0\}\\b)\\\frac{6x^{2} }{4x^{2} -9} \cdot \frac{2x+3}{3x^{2} -9x} =\frac{6x^{2} }{(2x-3)(2x+3)} \cdot\frac{2x+3}{3x(x-3)} =\frac{2x}{(2x-3)(x-3)} \\x\neq -\frac{3}{2} \quad x\neq 0\quad x\neq \frac{3}{2} \quad x\neq 3\\[/tex]
[tex]c)\\\displaystyle \frac{x^{3}+8 }{3x^{2} -3} \cdot\frac{6x+6}{x^{2} -2x+4} =\frac{(x+2)(x^{2} -2x+4)}{3(x-1)(x+1)} \cdot\frac{6(x+1)}{x^{2} -2x+4} =\frac{2(x+2)}{x-1} \\x\neq -1\quad x\neq 1\\d)\\\frac{2x^{2}+5x-3 }{10x-20} :\frac{4x^{2} -1}{3x-6} =\frac{(2x-1)(x+3)}{10(x-2)} :\frac{(2x-1)(2x+1)}{3(x-2)} =\\\frac{(2x-1)(x+3)}{10(x-2)}\cdot\frac{3(x-2)}{(2x-1)(2x+1)} =\frac{3(x+3)}{10(2x+1)} \\x\neq -\frac{1}{2} \quad x\neq \frac{1}{2} \quad x\neq 2[/tex]
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Odpowiedź:
[tex]\displaystyle \frac{x}{x+2}- \frac{3x+1}{3x} =\frac{3x^2-(3x+1)(x+2)}{3x(x+2)} =\frac{3x^{2} -3x^{2} -7x-2}{3x(x+1)} =\\\frac{-7x-2}{3x(x+1)} \qquad D=R-\{-1,0\}\\b)\\\frac{6x^{2} }{4x^{2} -9} \cdot \frac{2x+3}{3x^{2} -9x} =\frac{6x^{2} }{(2x-3)(2x+3)} \cdot\frac{2x+3}{3x(x-3)} =\frac{2x}{(2x-3)(x-3)} \\x\neq -\frac{3}{2} \quad x\neq 0\quad x\neq \frac{3}{2} \quad x\neq 3\\[/tex]
[tex]c)\\\displaystyle \frac{x^{3}+8 }{3x^{2} -3} \cdot\frac{6x+6}{x^{2} -2x+4} =\frac{(x+2)(x^{2} -2x+4)}{3(x-1)(x+1)} \cdot\frac{6(x+1)}{x^{2} -2x+4} =\frac{2(x+2)}{x-1} \\x\neq -1\quad x\neq 1\\d)\\\frac{2x^{2}+5x-3 }{10x-20} :\frac{4x^{2} -1}{3x-6} =\frac{(2x-1)(x+3)}{10(x-2)} :\frac{(2x-1)(2x+1)}{3(x-2)} =\\\frac{(2x-1)(x+3)}{10(x-2)}\cdot\frac{3(x-2)}{(2x-1)(2x+1)} =\frac{3(x+3)}{10(2x+1)} \\x\neq -\frac{1}{2} \quad x\neq \frac{1}{2} \quad x\neq 2[/tex]