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March 18th, 2017, 06:32 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^212x+15)/〖(x3)〗^2 ;x≠3, show that the function can be written as f(x)=(3)/〖(x3)〗^2 +2;x≠3

March 18th, 2017, 06:46 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,780 Thanks: 919 
$f(x) = \dfrac{2x^2  12x + 15}{(x3)^2},~x \neq 3$ $2(x3)^2 = 2(x^2  6x + 9) = 2x^2 12x + 18 $ $2x^2  12x + 15 = 2(x3)^2  3$ $f(x) = \dfrac{ 2(x3)^2  3}{(x3)^2} = $ $\dfrac{2(x3)^2}{(x3)^2}\dfrac {3}{(x3)^2} = $ $2 \dfrac{3}{(x3)^2}$ 
March 18th, 2017, 06:50 PM  #3 
Senior Member Joined: May 2016 From: USA Posts: 916 Thanks: 366 
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, 07:00 PM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,757 Thanks: 1008 Math Focus: Elementary mathematics and beyond 
$$\frac{2x^212x+15}{(x3)^2}=\frac{2x^211x+15x}{(x3)^2}=\frac{2x5}{x3}\frac{x}{(x3)^2}$$ $$\frac{2x6+1}{x3}=2+\frac{1}{x3},\,2+\frac{1}{x3}\frac{x}{(x3)^2}=2+\frac{3}{(x3)^2}$$ 
March 18th, 2017, 07:36 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


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