# Where is the hole in this rational function #f(x) = (x^2 + 2x - 8) / (x^2 - x - 2)#?

##### 1 Answer

Hole is a 'common' term for removable discontinuities for a rational function

**Step I** : We need to factorize the polynomials in the numerator and denominator.

Given

**Step 2** : We need to identify the common factor with same multiplicity in numerator and denominator, elimination of which from both the numerator and denominator makes the function defined for that particular value of

In our present case, both numerator and denominator contains the factor

**is a removable discontinuity.**

So, the hole of our function is