Simplify (x^2-5x+6)/(x^2-4)*(x^2+3x+2)/(x^2-2x-3)

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 ${\displaystyle -5}$.

Write the factored form using these integers.

Rewrite ${\displaystyle 4}$ as ${\displaystyle 2^2}$.

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 ${\displaystyle b=2}$.

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 ${\displaystyle 2}$ and whose sum is ${\displaystyle 3}$.

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 ${\displaystyle -3}$ and whose sum is ${\displaystyle -2}$.

Write the factored form using these integers.

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

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

Multiply ${\displaystyle \frac{x-2}{x-2}}$ by ${\displaystyle \frac{x+1}{x+1}}$.

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

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