Question
Simplify the expression (x-\dfrac{2x}{x-1})÷\dfrac{x^2-2x+1}{x^2-1}
Answer
(x-\dfrac{2x}{x-1})÷\dfrac{x^2-2x+1}{x^2-1}
=\dfrac{x(x-1)-2x}{x-1} ÷\dfrac{(x-1)^2}{x^2-1}
=\dfrac{x^2-3x}{x-1} \cdotp (x-1)
=x^2-3x
Simplify the expression (x-\dfrac{2x}{x-1})÷\dfrac{x^2-2x+1}{x^2-1}
(x-\dfrac{2x}{x-1})÷\dfrac{x^2-2x+1}{x^2-1}
=\dfrac{x(x-1)-2x}{x-1} ÷\dfrac{(x-1)^2}{x^2-1}
=\dfrac{x^2-3x}{x-1} \cdotp (x-1)
=x^2-3x