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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: 7,674 Thanks: 2654 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. Tags simplify Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Chikis Algebra 7 July 10th, 2014 07:15 PM mared Algebra 1 July 10th, 2014 07:36 AM ineedhelpnow Algebra 2 July 10th, 2014 05:30 AM Chikis Algebra 2 July 9th, 2014 11:33 PM Ronaldo Complex Analysis 1 December 31st, 1969 04:00 PM

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