Re: [Math4u] Re: Rational expressions

Problem:

2x/(1-2x) + 3x/(2x+1) - 3/(4x^2-1)

Solution:

We must get all the bottom numbers to be the same. Notice that

(2x-1)*(2x+1)=4x^2-1

So we need to get all three fractions so they have 4x^2-1 on the bottom. We multiply the top and bottom of the first fraction by -(2x+1). We multiply the top and bottom of the second fraction by (2x-1). Now all three fractions have 4x^2-1 on the bottom.

-2x*(2x+1)/(4x^2-1) + 3x*(2x-1)/(4x^2-1) - 3/(4x^2-1)

We group together the top numbers using the distributive law

=[-2x*(2x+1) + 3x*(2x-1) - 3] / (4x^2-1)

simplify

=[(-4x2-2x) + (6x^2-3x) - 3] / (4x^2-1)

simplify

=[(2x^2 - 5x-3] / (4x^2-1)

factor

=[(2x+1)*(x-3)] / [(2x-1)*(2x+1)]

divide top and bottom by (2x+1)

=(x-3)/(2x-1) ANSWER

check, let's say x=5

10/-9 + 15/11 -3/99 = -110/99 + 135/99 - 3/99 = 22/99=2/9

5 / 11

=[(2x^2 - 5x-3] / (4x^2-1)=22/99=2/9

=[(-4x2-2x) + (6x^2-3x) - 3] / (4x^2-1)=[-110+135-3]/99=2/9

=(x-3)/(2x-1) =2/9

OK, these checks are out of order because I found I made several mistakes and used the checks to find and correct my mistakes. It is difficult for me now and more difficult when I was an unpracticed student in a state of panic.

regards,

Brian

 

----- Original Message -----

From: trayc2244

To: Math4u@yahoogroups.com

Sent: Monday, October 01, 2007 7:29 PM

Subject: [Math4u] Re: Rational expressions

The problem is the teacher explains things as if I already know this
stuff. Can you work this problem out for me (the easiest way)

2x + 3x - 3
_______ _______ _______
1 - 2x 2x + 1 4x(squared)-1 ...the 4x is squared

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