Answer:
(9 - 4 x)/(x (2 x - 4))
Step-by-step explanation:
Simplify the following:
1/(2 x^2 - 4 x) - 2/x
Put each term in 1/(2 x^2 - 4 x) - 2/x over the common denominator x (2 x - 4): 1/(2 x^2 - 4 x) - 2/x = ((x (2 x - 4))/(2 x^2 - 4 x))/(x (2 x - 4)) - (2 (2 x - 4))/(x (2 x - 4)):
((x (2 x - 4))/(2 x^2 - 4 x))/(x (2 x - 4)) - (2 (2 x - 4))/(x (2 x - 4))
A common factor of 2 x - 4 and 2 x^2 - 4 x is 2 x - 4, so (x (2 x - 4))/(2 x^2 - 4 x) = (x (2 x - 4))/(x (2 x - 4)):
((x (2 x - 4))/(x (2 x - 4)))/(x (2 x - 4)) - (2 (2 x - 4))/(x (2 x - 4))
(x (2 x - 4))/(x (2 x - 4)) = 1:
1/(x (2 x - 4)) - (2 (2 x - 4))/(x (2 x - 4))
1/(x (2 x - 4)) - (2 (2 x - 4))/(x (2 x - 4)) = (1 - 2 (2 x - 4))/(x (2 x - 4)):
(1 - 2 (2 x - 4))/(x (2 x - 4))
-2 (2 x - 4) = 8 - 4 x:
(8 - 4 x + 1)/(x (2 x - 4))
Add like terms. 1 + 8 = 9:
Answer: (9 - 4 x)/(x (2 x - 4))
