H(x)= (x^2 -36)/x +6 explain why the following function is not continuous at x=-6

You can solve this problem through factoring.

First, you have the equation,

Then, you can factor the numerator.

You can cancel out the x-6 in both the numerator and the denominator because they would equal to just 1.

You are left with

The function is removable noncontinuous at x=6 because if you plug in 6 in x-6, your denominator would be undefined.

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.