The Goal

Simplify the expression:

The Mistake

Find the algebra mistake:

(Roll the mouse over the algebra to see a hint in red)

The Correction

(Roll the mouse over the area above to see the correction in blue)

An Explanation

Terms cannot simply be pulled out of a square root expression. This expression cannot be simplified as shown in "The Mistake".
In calculus it is useful to "simplify" expressions (such as this one) as shown in "The Correction". The technique used here eliminates square roots from the numerator at the expense of introducing them in the denominator. You may have been told that square roots in the denominator should be removed by "rationalizing". While that is an important skill, sometimes it is beneficial to introduce or keep square root expressions in the denominator. In the expression here it allows both the numerator and denominator to be reduced to a form in which the limit can be computed as h appoaches 0.