$$\frac{6x\cdot4+4x\cdot3+2x\cdot2+x-2}{3x\cdot2+x-1} = 0$$
Answer
$$ x = \frac{2}{41} $$
Explanation
$$ \begin{aligned} \frac{6x\cdot4+4x\cdot3+2x\cdot2+x-2}{3x\cdot2+x-1} &= 0&& \text{multiply ALL terms by } \color{blue}{ 3x\cdot2+x-1 }. \\[1 em](3x\cdot2+x-1)\frac{6x\cdot4+4x\cdot3+2x\cdot2+x-2}{3x\cdot2+x-1} &= (3x\cdot2+x-1)\cdot0&& \text{cancel out the denominators} \\[1 em]41x-2 &= 0&& \text{ move the constants to the right } \\[1 em]41x &= 2&& \text{ divide both sides by $ 41 $ } \\[1 em]x &= \frac{2}{41}&& \\[1 em] \end{aligned} $$
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