Difference Quotient...HELP!!!

This is the problem that I have been struggling with the whole weekend:

**Find the difference quotient of:**

g(x) = (x+1) / (x-3)

**I have:**

g(x) = [ ( (x+h)+1/(x+h)-3 ) - (x+1)/(x-3) ] / h

**Problem:

Is the LCD

1) (x-3)(x+h)-3 or

2) (x-3)(x+h-3)

Because grouping changes the whole answer...also, if it's choice 1, is the (-3) at the end of the LCD multiplied times the numerators as well or is it just added after you multiply the rest of the LCD??

Help!!!

Re: Difference Quotient...HELP!!!

For your difference quotient, you should have:

$\displaystyle \frac{g(x+h)-g(x)}{h}=\frac{\frac{(x+h)+1}{(x+h)-3}-\frac{x+1}{x-3}}{h}$

Now, what do you think the LCD in the numerator of the difference quotient is?

Re: Difference Quotient...HELP!!!

LCD is ** (x-3)(x+h)-3 ** correct?

Re: Difference Quotient...HELP!!!

So when I multiply by the LCD to cancel out the small fractions, do i multiply it as:

(x-3)(x+h-3) or (x-3)(x+h)-3 ?

Re: Difference Quotient...HELP!!!

Use the first choice. Do you see that it has to be the product of the two denominators?

Re: Difference Quotient...HELP!!!

That's what I chose but I had a feeling a was doing it wrong.

My final answer is **-4**

Re: Difference Quotient...HELP!!!

That is the correct result for the numerator, after dividing out the factor of *h* common to the numerator and denominator of the difference quotient. So what is the denominator?

Re: Difference Quotient...HELP!!!

After multiplying by the LCD and adding/subtracting like terms, I got:

**-4h/h**

I then canceled out the h's to get **-4** as my overall final answer

Re: Difference Quotient...HELP!!!

You must also multiply the denominator of the difference quotient by the LCD, so that in effect you are multiplying the quotient by 1 in the form of LCD/LCD. Otherwise, you are changing the expression. Recall the multiplicative identity 1·*a* = *a*.