# How do you find the intercepts for F(x)=(x^2+x-12)/(x^2-4)?

Feb 19, 2016

x= -4 , x = 3 , y=3

#### Explanation:

When any function crosses the x-axis , the corresponding y-coordinate will be zero. By letting y = 0 , we can find the x-intercept.

hence : $\frac{{x}^{2} + x - 12}{{x}^{2} - 4} = 0$

now for this rational function to be zero . it can only be from the numerator as division by zero is undefined.

$\Rightarrow {x}^{2} + x - 12 = 0$
factor and solve.

(x+ 4 )(x - 3 ) = 0 → x = - 4 , x = 3

Similarly , when the function crosses the y-axis , let x = 0.

rArr y =( -12)/-4 = 3 → y = 3