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 August 3rd, 2016, 09:59 AM #1 Member   Joined: Jul 2016 From: Usa Posts: 59 Thanks: 3 How to simplify this? This is the problem ((1/x+h-1)-(1/x-1))/h.
 August 3rd, 2016, 10:12 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,657 Thanks: 2635 Math Focus: Mainly analysis and algebra ${{1 \over x+h-1}-{1 \over x-1} \over h}$? You should make sure that you use parenthesis properly in writing out your problems. I would start by performing the subtraction in the numerator. What have you tried? How far did you get?
August 3rd, 2016, 10:40 AM   #3
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 Originally Posted by v8archie ${{1 \over x+h-1}-{1 \over x-1} \over h}$? You should make sure that you use parenthesis properly in writing out your problems. I would start by performing the subtraction in the numerator. What have you tried? How far did you get?
So I was given f(x)= 1/x-1 find in simplest terms (f(x+h)-f(x))/h.
I got to (x-1)-(x+h-1)/(x+h-1)(x-1) as the numerator.

August 3rd, 2016, 11:11 AM   #4
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 Originally Posted by Pete23 So I was given f(x)= 1/x-1 find in simplest terms (f(x+h)-f(x))/h. I got to (x-1)-(x+h-1)/(x+h-1)(x-1) as the numerator.
I am still not sure whether you mean $f(x) = \dfrac{1}{x} - 1$ or $f(x) = \dfrac{1}{x - 1}.$

Assuming the latter

$f(x + h) = \dfrac{1}{x + h - 1}.$

So $f(x + h) - f(x) = \dfrac{1}{x + h - 1} - \dfrac{1}{x - 1} = \dfrac{(x - 1) - (x + h - 1)}{(x + h - 1)(x - 1)} = \dfrac{-\ h}{(x + h - 1)(x - 1)}.$

Now what?

Last edited by JeffM1; August 3rd, 2016 at 11:13 AM.

August 3rd, 2016, 11:34 AM   #5
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 Originally Posted by Pete23 I got to (x-1)-(x+h-1)/(x+h-1)(x-1) as the numerator.
Good. You are nearly there. Simplify the numerator of that, and then divide by $h$ (your original denominator).

August 3rd, 2016, 11:51 AM   #6
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 Originally Posted by v8archie Good. You are nearly there. Simplify the numerator of that, and then divide by $h$ (your original denominator).
Is the numerator just 1?

August 3rd, 2016, 12:24 PM   #7
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 Originally Posted by Pete23 Is the numerator just 1?
When you simplify $(x + 1) - (x + h - 1)$ you get MINUS h.

So the numerator when you divide by h is MINUS 1.

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