## Difference Quotient

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.

### Difference Quotient

Hi All,

Trying to understand how to work to work this problem for a difference quotient. The problem was this:

$\frac{(x+h)^2 + \sqrt{x+h} - (x^2 + \sqrt{x})}{h}$

After simplifying, I am left with:

$h + 2x + \sqrt{x+h} + \sqrt{x}$

But the answer to the problem was:

$h + 2x + \frac{1}{\sqrt{x+h} + \sqrt{x}}$

I guess I dont understand why the 1 was placed above $\sqrt{x+h} + \sqrt{x}$. I know that when I cancelled out the common factor "h" I should have done something with the radicals but Im not quite sure what and I guess I dont understand how this part was worked. Any help is appreciated.
math_apprentice

Posts: 1
Joined: Fri Aug 30, 2013 4:02 pm

### Re: Difference Quotient

math_apprentice wrote:$\frac{(x+h)^2 + \sqrt{x+h} - (x^2 + \sqrt{x})}{h}$

After simplifying, I am left with:

$h + 2x + \sqrt{x+h} + \sqrt{x}$

What were your steps between these two lines? Because I get the same thing the book does.
FWT

Posts: 73
Joined: Sat Feb 28, 2009 8:53 pm

### Re: Difference Quotient

math_apprentice,

Tell the given function that you are using to form the difference quotient. We could make better sense of the needed steps if we know the given function.
jg.allinsymbols

Posts: 75
Joined: Sat Dec 29, 2012 2:42 am