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