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Algebra 50 Online
OpenStudy (cbreadbox):

I need help with this difference quotient problem. I've already constructed it, but I don't know where to start. Find the difference quotient for the function

OpenStudy (cbreadbox):

\[f(x)=\frac{ 1 }{ x-2 }\]

OpenStudy (mathmale):

Now that you've defined f(x), find f(x+h). That is, starting with f(x) = 1 / (x-2), replace each "x" with "(x+h)."

OpenStudy (mathmale):

Next, form f(x+h)-f(x). Last, divide your result by h. You will then have a difference and you'll also have a quotient .... thus, a "difference quotient."

OpenStudy (cbreadbox):

so I know the difference quotient itself.\[\frac{ f(x+h)-f(x) }{ h }\] And I constructed it:\[\frac{ \frac{ 1 }{ (x+h)-2}-\frac{ 1 }{ x-2 } }{ h }\] I just don't know where to start

OpenStudy (cbreadbox):

They want me to simplify it

OpenStudy (mathmale):

Actually, you have already done the minimum work necessary to produce a "difference quotient." If you want to proceed further, you'll need to add together the 2 fractions. This means identifying and using the Lowest Common Denominator.

OpenStudy (mathmale):

Hint: Multiply the first fraction by \[\frac{ x-2 }{ x-2 }\]

OpenStudy (mathmale):

and multiply the 2nd fraction by \[\frac{ x+h-2 }{ x+h-2 }\]

OpenStudy (mathmale):

Through your doing this you will have created 2 fractions with the same denominator, which is (x-2)(x+h-2). Combine like terms in the numerator. If done correctly, you will come up with an "h" in the numerator that can be cancelled out by the "h" in the denominator of the overall fraction.

OpenStudy (mathmale):

Hate to say this, but I need to get off OpenStudy and go to sleep. If you have an urgent question, ask it now, please.

OpenStudy (cbreadbox):

I think I got it, but thank you.

OpenStudy (mathmale):

My pleasure. Please complete the problem, so that I can see your solution tomorrow.

OpenStudy (cbreadbox):

okay

OpenStudy (cbreadbox):

\[\frac{ 2x+h }{ h }\] Am I right?

OpenStudy (cbreadbox):

Or\[\frac{ x+h-4 }{ h }\]

OpenStudy (triciaal):

I don't think you are suppose to have h in your answer

OpenStudy (cbreadbox):

the course i'm taking is college algebra math 121. I'm constructing and simplifying the difference quotient for a function. but i guess i'll look into that to be sure.

OpenStudy (cbreadbox):

Real quick I need to know which answer is right?

zepdrix (zepdrix):

Hmm neither looks correct.

zepdrix (zepdrix):

\[\large\rm \frac{\frac{1}{x+h-2}-\frac{1}{x-2}}{h}\color{royalblue}{\left[\frac{(x-2)(x+h-2)}{(x-2)(x+h-2)}\right]}\]Multiplying through by the least common multiple of our denominators gives us,\[\large\rm \frac{(x-2)-(x+h-2)}{h(x-2)(x+h-2)}\]The numerator will simplify very nicely, leaving a bunch of stuff in the denominator.

OpenStudy (mathmale):

If you'd please share your work, it'd be much easier for others to give you feedback. The quantity 'h' MUST cancel as you write and simplify the difference quotient.

OpenStudy (mathmale):

Could you take a snapshot of your work and share that snapshot here? It's too messy and time consuming to look at just parts of your work piecemeal.

OpenStudy (mathmale):

I agree with zepdrix' final expression, above. It needs to be simplified. @cbreadbox : would you please take responsibility for simplifying that expression. you will have 'h' in both numerator and denom and should cancel appropriately.

OpenStudy (mathmale):

I am closing this discussion due to lack of response from you.

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