Simplify (x^2-1)/(x^2+5x+4)*(x^2)/(x^2-x)

Rewrite ${\displaystyle 1}$ as ${\displaystyle 1^2}$.

Since both terms are perfect squares, factor using the difference of squares formula, ${\displaystyle a^2-b^2=(a+b)(a-b)}$ where ${\displaystyle a=x}$ and ${\displaystyle b=1}$.

Consider the form ${\displaystyle x^2+bx+c}$. Find a pair of integers whose product is ${\displaystyle c}$ and whose sum is ${\displaystyle b}$. In this case, whose product is ${\displaystyle 4}$ and whose sum is ${\displaystyle 5}$.

Write the factored form using these integers.

Factor ${\displaystyle x}$ out of ${\displaystyle x^2-x}$.

Combine.

Cancel the common factor of ${\displaystyle x+1}$.

Cancel the common factor of ${\displaystyle x-1}$.

Cancel the common factor of ${\displaystyle x^2}$ and ${\displaystyle x}$.