Find the x and y Intercepts f(x)=(x^2+8x+12)/(5x^2+34x+45)

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 ${\displaystyle 8}$.

Write the factored form using these integers.

Set ${\displaystyle x+2}$ equal to ${\displaystyle 0}$.

Subtract ${\displaystyle 2}$ from both sides of the equation.

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

Subtract ${\displaystyle 6}$ from both sides of the equation.

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

Multiply ${\displaystyle 8}$ by ${\displaystyle 0}$.

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

Add ${\displaystyle 0}$ and ${\displaystyle 12}$.

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

Multiply ${\displaystyle 5}$ by ${\displaystyle 0}$.

Multiply ${\displaystyle 34}$ by ${\displaystyle 0}$.

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

Add ${\displaystyle 0}$ and ${\displaystyle 45}$.

Factor ${\displaystyle 3}$ out of ${\displaystyle 12}$.

Cancel the common factors.