Hi,
a)
$$x-\frac{x}{x-2}+2 = 5x \quad|\cdot (x-2)$$
$$x(x-2) - x + 2(x-2) = 5x(x-2)$$
$$x^2-2x-x+2x-4 = 5x^2-10x |\quad -x^2+x+4$$
$$4x^2-9x+4 = 0 \quad|\text{:4, dann pq-Formel}$$
$$x_{1,2} = \frac98\pm\frac{\sqrt{17}}{8}$$
b)
$$\frac{4}{x-1} - \frac{x}{x+2} + 3 = 0\quad|\cdot(x-1)(x+2)$$
$$4(x+2) - x(x-1) + 3(x-1)(x+2) = 0$$
$$4x+8 - x^2 + x + 3x^2+3x-6 = 0$$
$$2x^2 + 8x +2 = 0\quad|\text{:2, dann pq-Formel}$$
$$x_{1,2} = -2\pm\sqrt3$$
Grüße