What is the x (4/x+2)+(1/x-2) = (5x-6)/(x^2-4)?

Then we have 4/x + 2 + 1/x - 2 = (5x - 6)/(x² - 4)  and we must have x≠0, x≠2, x≠-2

5/x = (5x - 6)/(x² - 4)

Multiply both sides by (x² - 4)*x

5(x² - 4) = (5x - 6)x

5x² - 20 = 5x² - 6x

-20 = -6x

x = 20/6

x = 10/3

$$x=3\frac{1}{3}$$

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Is the first term  $$\frac{4}{x}+2$$  or $$\frac{4}{x+2}$$ ?

Is the second term  $$\frac{1}{x}-2$$  or  $$\frac{1}{x-2}$$  ?

the second one. :)