[tex]\frac{x^{2} + 2x + 1}{x - 2} \div \frac{x^{2} - 1}{x^{2} - 4}[/tex]
[tex]\frac{x^{2} + x + x + 1}{x - 2} \div \frac{x^{2} + x - x - 1}{x^{2} + 2x - 2x - 4}[/tex]
[tex]\frac{x(x) + x(1) + 1(x) + 1(1)}{x - 2} \div \frac{x(x) + x(1) - 1(x) - 1(1)}{x(x) + x(2) - 2(x) - 2(2)}[/tex]
[tex]\frac{x(x + 1) + 1(x + 1)}{x - 2} \div \frac{x(x + 1) - 1(x + 1)}{x(x + 2) - 2(x + 2)}[/tex]
[tex]\frac{(x + 1)(x + 1)}{x - 2} \div \frac{(x - 1)(x + 1)}{(x - 2)(x + 2)}[/tex]
[tex]\frac{(x + 1)(x + 1)}{x - 2} \times \frac{(x - 2)(x + 2)}{(x - 1)(x + 1)}[/tex]
[tex]\frac{x + 1}{1} \times \frac{x + 2}{x - 1}[/tex]
[tex]\frac{x^{2} + 3x + 2}{x - 1}[/tex]
