For your difference quotient, you should have:
Now, what do you think the LCD in the numerator of the difference quotient is?
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!!!
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.