#### Question

Simplify the expression

(1+\dfrac{x^2-1}{x^2-2x+1} )÷\dfrac{1}{x-1}

Question

Simplify the expression

(1+\dfrac{x^2-1}{x^2-2x+1} )÷\dfrac{1}{x-1}

(1+\dfrac{x^2-1}{x^2-2x+1} )÷\dfrac{1}{x-1}

=[1+\dfrac{x-1)(x+1)}{(x-1)^2} ]\cdotp (x-1)

=( 1+x+1)(x-1)

=x^2+x-2