Hãy rút gọn: \(A = \sqrt {16x + 16}  - \sqrt {9\left( {x + 1} \right)}  \)\(\,+ \sqrt {25x + 25} \,\,\,\,\left( {x \ge  -

* Hướng dẫn giải

Ta có:

\(A = \sqrt {16x + 16}  - \sqrt {9\left( {x + 1} \right)}  \)\(\,+ \sqrt {25x + 25}\)

\(\begin{array}{l}
= \sqrt {16\left( {x + 1} \right)} - \sqrt {9\left( {x + 1} \right)} + \sqrt {25\left( {x + 1} \right)} \\
= \sqrt {{4^2}\left( {x + 1} \right)} - \sqrt {{3^2}\left( {x + 1} \right)} + \sqrt {{5^2}\left( {x + 1} \right)}
\end{array}\)

\( = 4\sqrt {x + 1}  - 3\sqrt {x + 1}  + 5\sqrt {x + 1}  \)\(\,= 6\sqrt {x + 1} \)