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 March 18th, 2017, 07:32 PM #1 Member   Joined: Mar 2017 From: Tasmania Posts: 36 Thanks: 2 Show that the function can be written as... a) Given the function f(x)=(2x^2-12x+15)/〖(x-3)〗^2 ;x≠3, show that the function can be written as f(x)=(-3)/〖(x-3)〗^2 +2;x≠3 March 18th, 2017, 07:46 PM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,646 Thanks: 1476 $f(x) = \dfrac{2x^2 - 12x + 15}{(x-3)^2},~x \neq 3$ $2(x-3)^2 = 2(x^2 - 6x + 9) = 2x^2 -12x + 18$ $2x^2 - 12x + 15 = 2(x-3)^2 - 3$ $f(x) = \dfrac{ 2(x-3)^2 - 3}{(x-3)^2} =$ $\dfrac{2(x-3)^2}{(x-3)^2}-\dfrac {3}{(x-3)^2} =$ $2 -\dfrac{3}{(x-3)^2}$ Thanks from topsquark and Posher March 18th, 2017, 07:50 PM #3 Senior Member   Joined: May 2016 From: USA Posts: 1,310 Thanks: 552 This is a little tricky. $\dfrac{2x^2 - 12x + 15}{(x - 3)^2} = \dfrac{2x^2 - 12x + 15 + 3 - 3}{(x - 3)^2} = \dfrac{2(x^2 - 6x + 9) - 3}{(x - 3)^2}.$ Now what? March 18th, 2017, 08:00 PM #4 Global Moderator   Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,979 Thanks: 1161 Math Focus: Elementary mathematics and beyond $$\frac{2x^2-12x+15}{(x-3)^2}=\frac{2x^2-11x+15-x}{(x-3)^2}=\frac{2x-5}{x-3}-\frac{x}{(x-3)^2}$$ $$\frac{2x-6+1}{x-3}=2+\frac{1}{x-3},\,2+\frac{1}{x-3}-\frac{x}{(x-3)^2}=2+\frac{-3}{(x-3)^2}$$ March 18th, 2017, 08:36 PM #5 Member   Joined: Mar 2017 From: Tasmania Posts: 36 Thanks: 2 @romsek thanks for this I managed to see how to do it legit like 10 minutes after posting your way was way the way I did it but missed out a few steps so thank you for showing me them Tags function, show, written 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 SenatorArmstrong Calculus 5 December 13th, 2016 09:55 PM Fanascom Calculus 8 October 23rd, 2013 07:39 AM Issler Real Analysis 2 February 22nd, 2012 09:06 AM mathman1990 Abstract Algebra 0 October 6th, 2011 05:48 AM honeyman Calculus 1 March 14th, 2010 10:31 AM

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