Simplify the expression given below. 1 / (2x^2-4x) - 2/x

A. - 3x-8/2x (x-2)

B. 4x-7/2x (x-2)

C. - 4x+9/2x (x-2)

D. - 1/2x (x-2)

(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))

Answer: The answer is C

-4x+9/2x (x-2)