Find the x and y Intercepts f(x)=(x^2+7x+10)/(2x^2-x-10)

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 ${\displaystyle 10}$ and whose sum is ${\displaystyle 7}$.

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 ${\displaystyle x+5}$ equal to ${\displaystyle 0}$.

Subtract ${\displaystyle 5}$ from both sides of the equation.

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

Multiply ${\displaystyle 7}$ by ${\displaystyle 0}$.

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

Add ${\displaystyle 0}$ and ${\displaystyle 10}$.

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

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

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

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

Subtract ${\displaystyle 10}$ from ${\displaystyle 0}$.