
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
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: Southern California, USA Posts: 1,413 Thanks: 717 
$f(x) = \dfrac{2x^2  12x + 15}{(x3)^2},~x \neq 3$ $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: 786 Thanks: 312 
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: 7,576 Thanks: 931 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


Tags 
function, show, written 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Best way to show that a function is onetoone  SenatorArmstrong  Calculus  5  December 13th, 2016 08:55 PM 
Integral that cannot be written in term of elem function  Fanascom  Calculus  8  October 23rd, 2013 06:39 AM 
Why can a periodic function be written as a Fourier Series?  Issler  Real Analysis  2  February 22nd, 2012 08:06 AM 
Show that every element of G can be written as such?  mathman1990  Abstract Algebra  0  October 6th, 2011 04:48 AM 
Given function, show that  honeyman  Calculus  1  March 14th, 2010 09:31 AM 