Find the x and y Intercepts R(x)=(x^2+x-12)/(x^2-x-6)

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.

Set ${\displaystyle x-3}$ equal to ${\displaystyle 0}$.

Add ${\displaystyle 3}$ to both sides of the equation.

Set ${\displaystyle x+4}$ equal to ${\displaystyle 0}$.

Subtract ${\displaystyle 4}$ from both sides of the equation.

Raising ${\displaystyle 0}$ to any positive power yields ${\displaystyle 0}$.

Add ${\displaystyle 0}$ and ${\displaystyle 0}$.

Subtract ${\displaystyle 12}$ from ${\displaystyle 0}$.

Raising ${\displaystyle 0}$ to any positive power yields ${\displaystyle 0}$.

Multiply ${\displaystyle -1}$ by ${\displaystyle 0}$.

Add ${\displaystyle 0}$ and ${\displaystyle 0}$.

Subtract ${\displaystyle 6}$ from ${\displaystyle 0}$.