Đáp án:
Giải thích các bước giải:
$\begin{array}{l}
a)\,\frac{2}{3}\sqrt {9x + 27} - \frac{3}{2}\sqrt {4x + 12} = \sqrt {3 + x} \,\,\,\left( {DK:x \ge - 3} \right)\\
\Leftrightarrow \frac{2}{3}.3\sqrt {x + 3} - \frac{3}{2}.2\sqrt {x + 3} - \sqrt {x + 3} = 0\\
\Leftrightarrow \sqrt {x + 3} \left( {2 - 3 - 1} \right) = 0\\
\Leftrightarrow \sqrt {x + 3} = 0\\
\Leftrightarrow x = - 3\left( {tm} \right)\\
b)\,\,\sqrt {25{x^2} - 30x + 9} = x - 1\\
\Leftrightarrow \sqrt {{{\left( {5x - 3} \right)}^2}} = x - 1\,\,\\
\Leftrightarrow \left| {5x - 3} \right| = x - 1\\
\Leftrightarrow \left[ \begin{array}{l}
5x - 3 = x - 1\,\,\,\left( {x \ge 1} \right)\\
5x - 3 = 1 - x\,\,\,\left( {x < 1} \right)
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{1}{2}\left( {ktm} \right)\\
x = \dfrac{2}{3}\left( {tm} \right)
\end{array} \right.
\end{array}$
