Answer: [tex]\bold{(C)\ \dfrac{3 - x}{x(x-1)}}[/tex]
Step-by-step explanation:
[tex]\dfrac{2}{x^2-x}-\dfrac{1}{x}[/tex]
[tex]=\dfrac{2}{x(x-1)}+\dfrac{-1}{x}[/tex]
[tex]=\dfrac{2}{x(x-1)}+\dfrac{-1}{x}\bigg(\dfrac{x-1}{x-1}\bigg)[/tex]
[tex]=\dfrac{2}{x(x-1)}+\dfrac{-x+1}{x(x-1)}[/tex]
[tex]=\dfrac{2-x+1}{x(x-1)}[/tex]
[tex]=\dfrac{3-x}{x(x-1)}[/tex]
The simplified form of 2/x^2-x - 1/x is (3-x)/(x(x-1)) , Option C is the correct answer.
What is an Expression ?
An expression is a mathematical statement consisting of a variables , constant and mathematical operators all simultaneously.
The expression given in the question is
[tex]\rm \dfrac{2}{x^{2} - x} - \dfrac{1}{x}\\\\\dfrac{2}{x(x-1)} + \dfrac{-1}{x}\\\\\\\dfrac{2}{x(x-1)} + \dfrac{-1}{x} (\dfrac{x-1}{x-1})\\\\\\\\dfrac{2}{x(x-1)} + \dfrac{-x +1}{x(x-1)}\\\\\\\dfrac{2-x+1}{x(x-1)}\\\\\dfrac{3-x}{x(x-1)}[/tex]
Therefore the simplified form of 2/x^2-x - 1/x is (3-x)/(x(x-1)), Option C is the correct answer.
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