Question

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

Answer 1

Answer:

The correct option is D.

Step-by-step explanation:

Consider the provided expression.

$\frac{1}{2x^2-4x}-\frac{2}{x}$

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

$\frac{x-2(2x^2-4x)}{x(2x^2-4x)}$

$\frac{x-4x^2+8x}{x(2x^2-4x)}$

$\frac{9x-4x^2}{x(2x^2-4x)}$

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

$\frac{9-4x}{2x^2-4x}$

$\frac{-4x+9}{2x(x-2)}$

Hence, the correct option is D.

Answer 2

Answer:

$\large\boxed{D.\ \dfrac{-4x+9}{2x(x-2)}}$

Step-by-step explanation:

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