Simplifying difference quotient.

AI Thread Summary
The discussion revolves around simplifying a difference quotient in a homework problem. The user initially multiplied by the least common denominator (LCD) but ended up with an incorrect numerator. After clarification, it was pointed out that the correct numerator should be 6x - 6 - 6x - 6h + 6. The final expression discussed is -6h - 7 over h(x + h - 1)(x - 1), with the correct numerator leading to further simplification. The conversation emphasizes the importance of accurately calculating both the numerator and denominator in the simplification process.
mistalopez
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Homework Statement



See attachment!

2. The attempt at a solution

I multiplied by the LCD of (x+h-1)(x-1) and got 6h/h(x+h-1)(x-1) . I then got 6h/h^2+2hx-2h . However, my answer seems to be wrong. What is my error?
 

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After you multiplied top and bottom by the LCD, the denominator is now h(x + h - 1)(x - 1).
What do you have for the numerator?
 
I got 6x-6-6x-6h-1 = -6h-7

The final answer -6h-7/h(x+h-1)(x-1)

Is that correct?
 
You have a mistake. The numerator should be 6x - 6 - 6x -6h + 6. As I already said, the denominator is h(x + h - 1)(x - 1).

What does all that simplify to?
 

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