Find the x and y Intercepts f(x)=(x^2+x-2)/((x+2)(x^2-2x-15))

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 ${\displaystyle 1}$.

Write the factored form using these integers.

Set ${\displaystyle x-1}$ equal to ${\displaystyle 0}$.

Add ${\displaystyle 1}$ to both sides of the equation.

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

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

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

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

Subtract ${\displaystyle 2}$ from ${\displaystyle 0}$.

Add ${\displaystyle 0}$ and ${\displaystyle 2}$.

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

Multiply ${\displaystyle -2}$ by ${\displaystyle 0}$.

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

Subtract ${\displaystyle 15}$ from ${\displaystyle 0}$.

Multiply ${\displaystyle 2}$ by ${\displaystyle -15}$.

Cancel the common factor of ${\displaystyle -2}$ and ${\displaystyle -30}$.