My Math Forum  

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

Algebra Pre-Algebra and Basic Algebra Math Forum


Thanks Tree3Thanks
  • 1 Post By Jomo
  • 1 Post By topsquark
  • 1 Post By JeffM1
Reply
 
LinkBack Thread Tools Display Modes
April 2nd, 2018, 02:51 PM   #1
Newbie
 
Joined: Mar 2018
From: Canada

Posts: 14
Thanks: 0

Least common denominator

Hi everyone.

The following is giving me some trouble.

(x^2 + 2x)/(x+2) + (x)/(x-1)

I’m supposed to find the LCD.

Here is what is giving me trouble.

Do I have to first factor the numerators and then find LCD?
( that would give me (x-1) as LCD)

If I don’t factor the numerators first, I believe I would get (x-1).(x+2) as my answer?

So my question is? Are both ways of doing it correct? Or should I actually always factor numerators first?
Can this expression have 2 LCD? Or it should always have just one ?

Thank you very much!

Last edited by Brunob; April 2nd, 2018 at 02:54 PM.
Brunob is offline  
 
April 2nd, 2018, 05:02 PM   #2
Senior Member
 
Joined: May 2016
From: USA

Posts: 1,310
Thanks: 551

$\dfrac{x^2 + 2x}{x + 2} + \dfrac{x}{x - 1} = \dfrac{(x^2 + 2x)(x - 1)}{(x + 2)(x - 1)} + \dfrac{(x + 2)x}{(x + 2)(x - 1)} =$

$\dfrac{x^3 - x^2 + 2x^2 - 2x + x^2 + 2x}{(x + 2)(x - 1)} = \dfrac{x^2(x + 2)}{(x + 2)(x - 1)} = \dfrac{x^2}{x - 1}.$

ALTERNATIVELY.

$\dfrac{x^2 + 2x}{x + 2} + \dfrac{x}{x - 1} = \dfrac{x(x + 2)}{x + 2} + \dfrac{x}{x - 1} =$

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

It makes absolutely no difference to the result which way you do it. They are equivalent. It is usually easier to simplify the fractions first if possible.
JeffM1 is offline  
April 2nd, 2018, 05:48 PM   #3
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 14,597
Thanks: 1038

Quote:
Originally Posted by Brunob View Post
(x^2 + 2x)/(x+2) + (x)/(x-1)

If I don’t factor the numerators first, I believe I would get (x-1).(x+2) as my answer?
That is not correct (as Jeff told you) BUT you could
have known that by assigning a value to x, like x=5; then:

(x^2 + 2x)/(x+2) + (x)/(x-1) = 6.25

(x-1).(x+2) = 28

Doing this during simplification tells you if
you're on the right path or not...get it, tabarnak?!
Denis is offline  
April 2nd, 2018, 07:22 PM   #4
Newbie
 
Joined: Nov 2013

Posts: 28
Thanks: 8

Quote:
Originally Posted by Denis View Post
That is not correct (as Jeff told you) BUT you could
have known that by assigning a value to x, like x=5; then:

(x^2 + 2x)/(x+2) + (x)/(x-1) = 6.25

(x-1).(x+2) = 28

Doing this during simplification tells you if
you're on the right path or not...get it, tabarnak?!
Denis, You are mistaken. The OP just asked for the LCD and claimed the answer (x-1).(x+2) is correct. As a result your substitution was not necessary. So what do you have to say about them apples?
Jomo is offline  
April 2nd, 2018, 07:26 PM   #5
Newbie
 
Joined: Nov 2013

Posts: 28
Thanks: 8

Quote:
Originally Posted by Brunob View Post
Hi everyone.

The following is giving me some trouble.

(x^2 + 2x)/(x+2) + (x)/(x-1)

I’m supposed to find the LCD.

Here is what is giving me trouble.

Do I have to first factor the numerators and then find LCD?
( that would give me (x-1) as LCD)

If I don’t factor the numerators first, I believe I would get (x-1).(x+2) as my answer?

So my question is? Are both ways of doing it correct? Or should I actually always factor numerators first?
Can this expression have 2 LCD? Or it should always have just one ?

Thank you very much!
I'll let you decide. You want the LEAST common Denominator and came up with two Common Denominators, namely (x-1).(x+2) and (x-1). And the least one is....?


Consider this problem: 2(x-3)/(x-3) + 3(x+7)/(x+7). How would you do this one? I would just do 2+3=5 and be done.

Last edited by Jomo; April 2nd, 2018 at 07:29 PM.
Jomo is offline  
April 3rd, 2018, 04:10 AM   #6
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 14,597
Thanks: 1038

Quote:
Originally Posted by Jomo View Post
Denis, You are mistaken. The OP just asked for the LCD and claimed the answer (x-1).(x+2) is correct. As a result your substitution was not necessary. So what do you have to say about them apples?
Whoops...that'll teach me to read a problem in full!!
I answered a different question
I'll go stand in the corner for (x-1)(x+2) minutes...
Thanks for the reprimand, Oh Jomo
Denis is offline  
April 3rd, 2018, 04:11 PM   #7
Newbie
 
Joined: Nov 2013

Posts: 28
Thanks: 8

Quote:
Originally Posted by Denis View Post
Thanks for the reprimand, Oh Jomo
You never have to worry about me missing an opportunity to reprimand Sir Denis.
Thanks from topsquark
Jomo is offline  
April 3rd, 2018, 06:00 PM   #8
Math Team
 
topsquark's Avatar
 
Joined: May 2013
From: The Astral plane

Posts: 2,226
Thanks: 908

Math Focus: Wibbly wobbly timey-wimey stuff.
Quote:
Originally Posted by Jomo View Post
You never have to worry about me missing an opportunity to reprimand Sir Denis.
And there are so many opportunities!

-Dan
Thanks from Denis
topsquark is offline  
April 3rd, 2018, 07:36 PM   #9
Senior Member
 
Joined: May 2016
From: USA

Posts: 1,310
Thanks: 551

Quote:
Originally Posted by Jomo View Post
two Common Denominators, namely (x-1).(x+2) and (x-1). And the least one is....?
Well if x = - 1, then (x - 1)(x + 2) = - 2 * 1 = - 2. But (x - 1) = - 2. Which is lesser? Under those circumstances [2(x - 1)(x + 2)]/2 would be less than either, so they certainly aren't least.

It is, I think, a very stupid question. I suspect that what was meant was the simplest common denominator. In any case, I carefully avoided answering it.
Thanks from topsquark

Last edited by JeffM1; April 3rd, 2018 at 07:39 PM.
JeffM1 is offline  
April 4th, 2018, 06:08 PM   #10
Newbie
 
Joined: Mar 2018
From: Canada

Posts: 14
Thanks: 0

Thanks everyone!
Brunob is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
algebra precalculus, common, denominator, lcd



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Product Of The Least Common Multiple and Greatest Common Factor Of Whole Numbers EvanJ Elementary Math 1 October 25th, 2015 08:06 AM
Need help with Highest Common Factor and Lowest Common Multiple QUestion blurgirl Elementary Math 5 July 15th, 2014 07:07 AM
common denominator Alexander4444 Algebra 2 November 6th, 2011 06:54 PM
common denominator in two values xaventon Elementary Math 1 June 3rd, 2010 12:19 PM
New results : Least Common Multiple & Greatest Common Diviso Yuly Shipilevsky Number Theory 5 March 20th, 2009 11:37 AM





Copyright © 2019 My Math Forum. All rights reserved.