Question

How to solve this algebraically?

Answer 1

Ok so x+4-1 makes x-1 so i belive the answer could be 1/5 

Answer 2

I believe in order to solve this question, use L'Hopital's Rule, as both the top and bottom will equal 0/0. Which is not what we want. Basically take the derivative of the top expression and take the derivative of the bottom expression. So the derivative of top can be written as d(X)/dx - d(5)/dx and divide everything by the derivative bottom expression that you must take as d(X+4)^1/2/dx, as square root of X+4 is the same as (X+4)^1/2. So altogether it would be d(X+4)^1/2/dx - d(3)/dx. So after taking the derivative on the top it becomes 1-0= 1. Then taking the derivative of bottom will be 1/[2(X+4)^1/2] - 0 = the same thing. Plugging in 5 into the new expression with derived top and bottoms would be 1/1/[2(5+4)^1/2. Evaluating will give you the answer as 1/6.