Thread: 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!!!

For your difference quotient, you should have:



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

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

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 ?

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

That's what I chose but I had a feeling a was doing it wrong.
My final answer is -4

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?

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

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.