$$\frac{x}{x-1}+\frac{2x}{x-2}=3$$
$x = \frac{6}{5} = 1\frac{1}{5} = 1.2$
$$\left(x-2\right)x+\left(x-1\right)\times 2x=3\left(x-2\right)\left(x-1\right)$$
$$x^{2}-2x+\left(x-1\right)\times 2x=3\left(x-2\right)\left(x-1\right)$$
$$x^{2}-2x+\left(2x-2\right)x=3\left(x-2\right)\left(x-1\right)$$
$$x^{2}-2x+2x^{2}-2x=3\left(x-2\right)\left(x-1\right)$$
$$3x^{2}-2x-2x=3\left(x-2\right)\left(x-1\right)$$
$$3x^{2}-4x=3\left(x-2\right)\left(x-1\right)$$
$$3x^{2}-4x=\left(3x-6\right)\left(x-1\right)$$
$$3x^{2}-4x=3x^{2}-9x+6$$
$$3x^{2}-4x-3x^{2}=-9x+6$$
$$-4x=-9x+6$$
$$-4x+9x=6$$
$$5x=6$$
$$x=\frac{6}{5}$$
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