Rút gọn biểu thức: \(\dfrac{{a + b}}{{{b^2}}}.\sqrt {\dfrac{{{a^2}{b^4}}}{{{a^2} + 2ab + {b^2}}}}\)

* Hướng dẫn giải

 \(\dfrac{{a + b}}{{{b^2}}}.\sqrt {\dfrac{{{a^2}{b^4}}}{{{a^2} + 2ab + {b^2}}}}\)

\(= \dfrac{{a + b}}{{{b^2}}}\sqrt {\dfrac{{{{\left( {a{b^2}} \right)}^2}}}{{{{\left( {a + b} \right)}^2}}}} \)

\(= \dfrac{{a + b}}{{{b^2}}} \cdot \dfrac{{\left| {a{b^2}} \right|}}{{ {a + b} }}\)

\( = \dfrac{{\left| a \right|.{b^2}}}{{{b^2}}} = \left| a \right|\)