can(4x+1)-can(3x-2)=x+3/5

\(\begin{array}{l}
\sqrt {4x + 1} – \sqrt {3x – 2} = \frac{{x + 3}}{5}\,\,\,\left( {DK:\,\,\, – \frac{1}{4} \le x \le \frac{2}{3}} \right)\\
Dat\,\,\sqrt {4x + 1} = a \ge 0;\sqrt {3x – 2} = b \ge 0\,\\
\Rightarrow {a^2} – {b^2} = x + 3\\
pt \Rightarrow a – b = \frac{{{a^2} – {b^2}}}{5}\\
\Leftrightarrow 5\left( {a – b} \right) – \left( {a + b} \right)\left( {a – b} \right) = 0\\
\Leftrightarrow \left( {a – b} \right)\left( {a + b – 5} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
a = b\\
a = 5 – b
\end{array} \right.\\
TH1:\,a = b \Leftrightarrow \sqrt {4x + 1} = \sqrt {3x – 2} \\
\Leftrightarrow 4x + 1 = 3x – 2 \Leftrightarrow x = – 3\left( {VL} \right)\\
TH2:\,a = 5 – b \Leftrightarrow \sqrt {4x + 1} = 5 – \sqrt {3x – 2} \\
\Rightarrow 4x + 1 = 25 + 3x – 2 – 10\sqrt {3x – 2} \\
\Leftrightarrow 10\sqrt {3x – 2} = 22 – x\,\,\left( {\frac{2}{3} \le x \le 22} \right)\\
\Leftrightarrow 100\left( {3x – 2} \right) = 484 – 44x + {x^2}\\
\Leftrightarrow {x^2} – 344x + 684 = 0\\
\Leftrightarrow \left( {x – 2} \right)\left( {x – 342} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x = 2\left( {tm} \right)\\
x = 342\left( {ktm} \right)
\end{array} \right.
\end{array}\)