Question

select the correct answer.

what is this expression in simplest form?

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

• \\(\frac{-4x + 9}{2x(x - 2)}\\)
• \\(\frac{-3x - 8}{2x(x - 2)}\\)
• \\(\frac{-1}{2x(x - 2)}\\)
• \\(\frac{4x - 7}{2x(x - 2)}\\)

Explanation:

Factor the denominators

$$ 2x^2 - 4x = 2x(x - 2) $$

Find a common denominator and subtract

$$
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Simplify the numerator

$$ \frac{1 - 4x + 8}{2x(x - 2)} = \frac{-4x + 9}{2x(x - 2)} $$

Answer:

• (A) \(\frac{-4x + 9}{2x(x - 2)}\) (Correct answer)
• (B) \(\frac{-3x - 8}{2x(x - 2)}\)
• (C) \(\frac{-1}{2x(x - 2)}\)
• (D) \(\frac{4x - 7}{2x(x - 2)}\)