Solution
- The solution steps are given below:
[tex]\begin{gathered} \frac{1}{2x^2-4x}-\frac{2}{x} \\ \\ \text{ We need to find the common denominator for both terms} \\ 2x^2-4x=2x(x-2)\text{ \lparen Denominator 1\rparen} \\ x\text{ \lparen Denominator 2\rparen} \\ \\ \text{ Both denominators have }2x(x-2)\text{ in common, thus, we can say:} \\ \\ \frac{1-2(2(x-2))}{2x(x-2)} \\ \\ \text{ Simplify:} \\ \frac{1-4x+8}{2x(x-2)} \\ \\ =\frac{9-4x}{2x(x-2)}=\frac{-4x+9}{2x(x-2)}\text{ \lparen OPTION C\rparen} \end{gathered}[/tex]
