Respuesta :

gmany

Answer:

[tex]\large\boxed{D.\ \dfrac{-4x+9}{2x(x-2)}}[/tex]

Step-by-step explanation:

[tex]\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)}[/tex]

Answer:

The correct option is D.

Step-by-step explanation:

Consider the provided expression.

[tex]\frac{1}{2x^2-4x}-\frac{2}{x}[/tex]

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

[tex]\frac{x-2(2x^2-4x)}{x(2x^2-4x)}[/tex]

[tex]\frac{x-4x^2+8x}{x(2x^2-4x)}[/tex]

[tex]\frac{9x-4x^2}{x(2x^2-4x)}[/tex]

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

[tex]\frac{9-4x}{2x^2-4x}[/tex]

[tex]\frac{-4x+9}{2x(x-2)}[/tex]

Hence, the correct option is D.

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