Thực hiện phép tính sau đây: \( \frac{{{x^2}}}{{{x^2} + 2x + 1}} - \frac{1}{{{x^2} + 2x + 1}} + \frac{2}{{x + 1}}\)

* Hướng dẫn giải

 \(\begin{array}{*{20}{l}} {\:\frac{{{x^2}}}{{{x^2} + 2x + 1}} - \frac{1}{{{x^2} + 2x + 1}} + \frac{2}{{x + 1}}\:\:\:\left( {x \ne - 1} \right)}\\ { = \frac{{{x^2}}}{{{x^2} + 2x + 1}} - \frac{1}{{{x^2} + 2x + 1}} + \frac{{2(x + 1)}}{{(x + 1)(x + 1)}}}\\ { = \frac{{{x^2}}}{{{x^2} + 2x + 1}} - \frac{1}{{{x^2} + 2x + 1}} + \frac{{2x + 2}}{{(x + 1)(x + 1)}}}\\ { = \frac{{{x^2} - 1 + 2x + 2}}{{{x^2} + 2x + 1}} = \frac{{{x^2} + 2x + 1}}{{{x^2} + 2x + 1}} = 1} \end{array}\)