SOLUTION: Rational expressions with different denominators 2x/x^2-9+3x/x^2+4x+3 I am confused on how to find a common denominator. I know for the first one it could be either 3x(x-3) o

Question 203367This question is from textbook
: Rational expressions with different denominators
2x/x^2-9+3x/x^2+4x+3
I am confused on how to find a common denominator. I know for the first one it could be either 3x(x-3) or (x-3)(x+3) for the second denominator i can only think of (x+3)(x+1) i just don't know which denominator is missing what.
I apprecate any help you can give me thank you This question is from textbook

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Rational expressions with different denominators
2x/x^2-9 + 3x/x^2+4x+3
----------------
You have to factor whereever you can so you can see the lcd:
---
(2x)/[(x-3)(x+3)] + (3x)/[(x+3)(x+1)]
-----
The lcd must contain each unique factor it its hghest power.
---
lcd = (x+1)(x+3)(x-3)
----------
Write each fraction over the lcd:
---
[(2x)(x+1)]/lcd + [(3x)(x+3)]/lcd
--------------------------------
Combine the numerators over the lcd:
---
[2x^2 + 2x + 3x^2+ 9x]/lcd
---
Simplify:
[5x^2 + 11x]/ [(x+1)(x+3)(x-3)]
======================================
Cheers,
Stan H.

RELATED QUESTIONS
I have been working on this all day. could someone explain this problem to me i am... (answered by Earlsdon)

I am trying to subtract a rational expression with an unlike denominator. Simplify the (answered by jim_thompson5910)

I am trying to add a rational expression with an unlike denominator. Simplify the... (answered by mananth)

How do I rewrite rational expressions in terms of a common denominator? 5x-1/4x(2x+1),... (answered by rothauserc)

I am still very confused on how to simplify rational expressions: This is the problem I... (answered by richwmiller,josmiceli)

I am trying to help my child but algebra was many years ago :-) . I have the answer but... (answered by drj)

I messed up and made my 1st question non-understandable. My sincerest apologies. please... (answered by josgarithmetic,MathTherapy)

A) Find the LCD, covert each rational expression into an equivalent expression with the... (answered by stanbon)

Solve each equation 3/x-2 + 1/x+2 =12/x2 - 4 I know that I need to find a... (answered by stanbon)