Find the x and y Intercepts (x^2+3x-54)/(x^2-9)

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 ${\displaystyle -54}$ and whose sum is ${\displaystyle 3}$.

Write the factored form using these integers.

Set ${\displaystyle x-6}$ equal to ${\displaystyle 0}$.

Add ${\displaystyle 6}$ to both sides of the equation.

Set ${\displaystyle x+9}$ equal to ${\displaystyle 0}$.

Subtract ${\displaystyle 9}$ from both sides of the equation.

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

Multiply ${\displaystyle 3}$ by ${\displaystyle 0}$.

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

Subtract ${\displaystyle 54}$ from ${\displaystyle 0}$.

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

Subtract ${\displaystyle 9}$ from ${\displaystyle 0}$.