Calculating+limits+using+algebra

If one can just plug in the x-value and get a number, then that is where the limit approaches. One must plug in numbers as they approach from both the left and right side of the x-value that the limit approaches only if just plugging in the x-value into the equation gives one an undefined number. Note: If the denominator equals zero, then make sure the fraction is in its simplest factored form and everything has been cancelled out that can be. When plugging in numbers, if the limit from the left does not approach the same number as the limit from the right, then the limit does not exist.