Answer: The required answer is [tex]\dfrac{x^2+3x+2}{x-1}.[/tex]
Step-by-step explanation: We are given to divide the following algebraic expression :
[tex]E=\dfrac{(x^2+2x+1)/(x-2)}{(x^2-1)/(x^2-4)}.[/tex]
We know that
[tex]\dfrac{a/b}{c/d}=\dfrac{a}{b}\times\dfrac{d}{c}.[/tex]
So, for the given expression E, we have
[tex]E\\\\\\=\dfrac{(x^2+2x+1)/(x-2)}{(x^2-1)/(x^2-4)}\\\\\\=\dfrac{x^2+2x+1}{x-2}\times\dfrac{x^2-4}{x^2-1}\\\\\\=\dfrac{(x+1)^2}{(x-2)}\times\dfrac{(x+2)(x-2)}{(x+1)(x-1)}\\\\\\=\dfrac{(x+1)(x+2)}{x-1}\\\\\\=\dfrac{x^2+3x+2}{x-1}.[/tex]
Thus, the required answer is [tex]\dfrac{x^2+3x+2}{x-1}.[/tex]
