Simplify ((x-1)^2)/(x^2-x-12)*(x^2+x-6)/(x^2-6x+5)

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 ${\displaystyle -12}$ and whose sum is ${\displaystyle -1}$.

Write the factored form using these integers.

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 ${\displaystyle -6}$ and whose sum is ${\displaystyle 1}$.

Write the factored form using these integers.

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 ${\displaystyle 5}$ and whose sum is ${\displaystyle -6}$.

Write the factored form using these integers.

Combine.

Cancel the common factor of ${\displaystyle {(x-1)}^2}$ and ${\displaystyle x-1}$.

Cancel the common factor of ${\displaystyle x+3}$.