Đáp án:
\(\left[ \begin{array}{l}
x = 6\\
x = - 1\\
x = 0
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
a)DK:x \ne \left\{ { - 8;5} \right\}\\
\dfrac{{6\left( {x + 8} \right)\left( {x - 8} \right) + \left( {x + 2} \right)\left( {x - 5} \right)\left( {x - 8} \right)}}{{\left( {x - 5} \right)\left( {x + 8} \right)\left( {x - 8} \right)}} = \dfrac{{ - 18\left( {x + 8} \right) - \left( {x - 5} \right)\left( {{x^2} - 64} \right)}}{{\left( {x - 5} \right)\left( {x + 8} \right)\left( {x - 8} \right)}}\\
\to 6\left( {{x^2} - 64} \right) + \left( {{x^2} - 3x + 10} \right)\left( {x - 8} \right) = - 18x - 144 - {x^3} + 64x + 5{x^2} - 320\\
\to 6{x^2} - 384 + {x^3} - 8{x^2} - 3{x^2} + 24x + 10x - 80 = - {x^3} + 5{x^2} + 46x - 464\\
\to 2{x^3} - 10{x^2} - 12x = 0\\
\to \left[ \begin{array}{l}
x = 6\\
x = - 1\\
x = 0
\end{array} \right.
\end{array}\)
