My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Thanks Tree2Thanks
  • 1 Post By mrtwhs
  • 1 Post By skipjack
Reply
 
LinkBack Thread Tools Display Modes
April 25th, 2014, 12:21 PM   #1
The
Newbie
 
Joined: Apr 2014
From: London

Posts: 13
Thanks: 1

Show that (fractions)

Show that (x+5)/((x-1)(x+2)) can be written as 2/(x-1)-1/(x+2).
Is there a specific tactic to approaching these questions or is it really straightforward?

Last edited by skipjack; April 25th, 2014 at 01:52 PM.
The is offline  
 
April 25th, 2014, 01:37 PM   #2
Senior Member
 
mrtwhs's Avatar
 
Joined: Feb 2010

Posts: 708
Thanks: 142

I believe you have a typo on the left hand side. The problem should read

$\displaystyle \dfrac{x+5}{(x-1)(x+2)} = \dfrac{2}{x-1}-\dfrac{1}{x+2}$.

What you want to do is called partial fractions. You can look this up online or in any reasonably good calculus book.
Thanks from The
mrtwhs is offline  
April 25th, 2014, 01:47 PM   #3
The
Newbie
 
Joined: Apr 2014
From: London

Posts: 13
Thanks: 1

Thank you sir, and no my book appears not to have this. Then again, it's not focused on calculus

Last edited by The; April 25th, 2014 at 01:48 PM. Reason: forgot how to english
The is offline  
April 25th, 2014, 02:30 PM   #4
Global Moderator
 
Joined: Dec 2006

Posts: 20,835
Thanks: 2162

I've corrected the errors in the original equation.

For information about partial fraction decomposition, follow the link or do a web search for easier articles about partial fractions.

The simplest decompositions are easily obtained in one step (with the aid of some mental arithmetic) by use of the cover-up rule.
Thanks from The

Last edited by skipjack; April 25th, 2014 at 04:29 PM.
skipjack is offline  
April 25th, 2014, 03:35 PM   #5
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,671
Thanks: 2651

Math Focus: Mainly analysis and algebra
Essentially, for partial fraction decomposition you write down the result with a number of unknown values and then solve a system of simultaneous equations for the solution.

In this case, we will write
$$\frac{x+5}{(x-1)(x+2)} = \frac{A}{x-1}+\frac{B}{x+2}$$
And then we multiply by the denominator on the left.
$$x+5=A(x+2) + B(x-1)$$
Now we compare coefficients of the different powers of $x$.
\begin{align*}
5 &= 2A - B &\text{from the units}\\
1 &= A + B &\text{from the coefficients of $x$}
\end{align*}
Thus we have two equations for two unknowns which we can therefore solve.

I encourage you to read more on the subject as it gets (a tiny bit) more complicated, but that approach will work for any denominator with distinct roots all of which are real (as long as the numerator is of lower order than the denominator).
v8archie is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
fractions, show


« fin | Simplify »

Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
help with fractions betweenthebars Algebra 2 October 11th, 2012 05:00 AM
want to show that show that two infinite summations R equal notnaeem Real Analysis 4 August 16th, 2010 12:32 PM
(4x-2)/2 * 3x/4 = ?? (Fractions) GrindingxxTeeth Algebra 1 January 4th, 2010 01:44 PM
Simplifying fractions with variables in fractions nova3421 Algebra 1 September 9th, 2009 10:03 AM
Different fractions mensamedlem Elementary Math 3 September 9th, 2008 05:18 PM





Copyright © 2019 My Math Forum. All rights reserved.