# Thread: Easy Rational Expression problems which I've completed and seeking review from peers

1. ## Easy Rational Expression problems which I've completed and seeking review from peers

Hi all,

Below are several problems I believe I have set up and solved correctly but would like for others to review them as well.

1). x / x^2 - 3x - 18 multiplied by x^2 - x - 12 / x^2 - 4x

= x / (x - 6) (x + 3) multiplied by (x - 4) (x + 3) / x (x - 4)

= 1 / x - 6 <-- I never factored in a LCD to get this answer, simply reduced.

2). x^2 - 3x - 4 / x^2 - 16 multiplied by x +4 / 3x - 9

= (x - 4) (x + 1) / (x + 4) (x - 4) multiplied by x + 4 / 3 (x - 3)

= x + 1 / 3 (x - 3) <-- Again, no LCD was factored into the equation, simple reduction only.

3). x - 3 / x + 2 divided by x^2 - x - 6

= x - 3 / x + 2 multiplied by 1 / (x - 3) (x + 2)

= 1 / (x + 2) (x + 2) or 1 / (x + 2)^2

4). 4 / x + 3 subtracted by 6 / 3x + 9

= 4 / x + 3 subtracted by 6 / 3 (x + 3); LCD equals 3 (x + 3)

= 3 (x + 3) times 4 / x + 3 subtracted by 6 / 3 (x + 3)

= 12 - 6 / 3 (x + 3) or 2 / x +3 when simplified

5). x + 3 / x^2 - x - 12 plus 2 / x +3 = 1 / x - 4

= x + 3 / (x - 4) (x + 3) plus 2 / x + 3 = 1 / x - 4; LCD = (x - 4) (x + 3)

= (x - 4) 2 = x + 3
= 2x - 8 = x + 3
2x = x + 11
x = 11

Is anyone able to verify that my equations are set up properly and with correct answers?

Thank you.

2. ## Re: Easy Rational Expression problems which I've completed and seeking review from pe

The first question second rational expression has been wrongly factorized. It should be (x+3)(x-4)/x(x-4) Now when you multiply you will get the correct answer i.e., 1/(x-6).
In second question answer use parenthesis to avoid confusion: (x+1)/[3(x-3)]
Third is correct. In fourth use brackets.
Fifth question is not clear

3. ## Re: Easy Rational Expression problems which I've completed and seeking review from pe

Originally Posted by ibdutt
The first question second rational expression has been wrongly factorized. It should be (x+3)(x-4)/x(x-4) Now when you multiply you will get the correct answer i.e., 1/(x-6).
In second question answer use parenthesis to avoid confusion: (x+1)/[3(x-3)]
Third is correct. In fourth use brackets.
Fifth question is not clear
Hi,

You are correct, the first question was not factored properly and I have since adjusted it.

The fifth question is meant to be solved. I have rewritten the equation, hopefully it is easier to read.

(x + 3) / [x^2 - x - 12] + 2 / (x + 3) = 1 / (x - 4).

4. ## Re: Easy Rational Expression problems which I've completed and seeking review from pe

Still it does not make sense. If we take it as it is then we have
(x+3)/[(x+3)(x-4) ] + 2/(x-3) = 1 / (x-4)
1/(x-4) + 2/(x-3) = 1 / (x-4)
2/(x-3) = 0 That just indicates that x is infinitely large

5. ## Re: Easy Rational Expression problems which I've completed and seeking review from pe

Originally Posted by ibdutt
Still it does not make sense. If we take it as it is then we have
(x+3)/[(x+3)(x-4) ] + 2/(x-3) = 1 / (x-4)
1/(x-4) + 2/(x-3) = 1 / (x-4)
2/(x-3) = 0 That just indicates that x is infinitely large
After factoring and reducing the equation aren't we left with the following:

x + 3 + 2x - 8 = x + 3

Combine like terms:

3x - 5 = x + 3

Subtract x from both sides:

2x - 5 = 3

2x = 8

Divide 2 to both sides:

x = 4

This answer is different than the original one I posted because I have since re-worked the problem.

However, when I plug 4 into all x values I end up with denominators equal to 0 which makes the equation 'invalid.'

Determining whether the equation has a solution or is invalid was part of the instructions so does x = 4 sound correct?

6. ## Re: Easy Rational Expression problems which I've completed and seeking review from pe

When is it necessary to arrange all terms and set to standard form?