Question

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

Answer 1

`\large\boxed{D.\ (-4x+9)/(2x(x-2))}`

Explanation:

`(1)/(2x^2-4x)-(2)/(x)=(1)/(2x(x-2))-(2)/(x)=(1)/(2x(x-2))-((2)(2)(x-2))/(2x(x-2))\\\\=(1-4(x-2))/(2x(x-2))\qquad\text{use the distributive property}\\\\=(1-4x+8)/(2x(x-2))=(-4x+9)/(2x(x-2))`

Answer 2

The correct option is D.

Explanation:

Consider the provided expression.

`(1)/(2x^2-4x)-(2)/(x)`

Now take the LCM of the denominator and solve the above expression as shown:

`(x-2(2x^2-4x))/(x(2x^2-4x))`

`(x-4x^2+8x)/(x(2x^2-4x))`

`(9x-4x^2)/(x(2x^2-4x))`

Cancel out the x as it is common in numerator and denominator.

`(9-4x)/(2x^2-4x)`

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

Hence, the correct option is D.