Originally Posted by
yeongil Multiply both sides by $\displaystyle 2(x - 4)(x + 3)(x - 1)$:
$\displaystyle \begin{aligned}
14(x - 1) - 8(x - 4) &= -3(x - 4)(x + 3)(x - 1) \\
14x - 14 - 8x + 32 &= -3x^3 + 6x^2 + 33x - 36 \\
6x + 18 &= -3x^3 + 6x^2 + 33x - 36 \\
0 &= -3x^3 + 6x^2 + 27x - 54 \\
0 &= -3(x^3 - 2x^2 - 9x + 18) \\
0 &= -3[x^2(x - 2) - 9(x - 2)] \\
0 &= -3(x - 2)(x^2 - 9) \\
0 &= -3(x - 2)(x + 3)(x - 3)
\end{aligned}$
You have solutions of x = 2, x = -3, and x = 3. Reject the solution x = -3.
x = 2, x = 3
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