Adding/subtracting rational expressions

[Havyn]

Thanks in advance to anyone who can help!

The problem:
Perform the addition or subtraction and simplify.
2x-1/x+4 - 1

It's my understanding that I'm supposed to find the LCD for the denominators. I'm just confused about how to do it when one denominator is (x+4) and the other is just 1. I thought maybe I would start like this:

(2x-1)(x+4)/(x+4)(x+4) and assume the the LCD is x+4. Then would the answer be 2x-2? I'm just really confused. ANY help is much appreciated!

 

[Denis]

Perform the addition or subtraction and simplify.
2x-1/x+4 - 1

Use BRACKETS please: (2x - 1) / (x + 4) + 1

(x + 4) / (x + 4) = 1, right? So:

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

Can you finish it?

 

[Havyn]

Is it (x+3)/(x+4)?

 

[jonboy]

Howdy, Havyn

Is it \(\displaystyle \L \;\frac{(x+3)}{(x+4)}\)?

Nope. This is why you show your work so we can see what you did wrong.

\(\displaystyle \L \;\frac{2x\,-\,1}{x\,+\,4}\,-\,\frac{x\,+\,4}{x\,+\,4}\,\)

Now you can put the negative sign on the denominator or the numerator of the second term, but in this case we need to put it on the numerator to keep the denominators the same to subtract.

So \(\displaystyle \L \;\frac{2x\,-\,1}{x\,+\,4}\,+\,\frac{\,-\,(x\,+\,4)}{x\,+\,4}\,\)

Now finish it up, and don't forget that Distributive Property!

 

[Havyn]

Thank you all for your help so far - you guys are life savers.

Unfortunately, I am now so massively confused I'm not really sure what to do next. It just seems like my book, my professor, this board, and everone else I talk to you says to do something different. If it were me on my own, and I had....

(2x-1)/(x+4) + -(x+4)/x+4 I would just add the numerators to get...

(x+3) and then the denominator is (x+4) but that gives me the same wrong answer I had before. Since you mentioned the distrubutive property, maybe I multiply?

so...

(-2x^2+4)/(x+4) is the answer?

 

[Denis]

Thank you all for your help so far - you guys are life savers.
Unfortunately, I am now so massively confused I'm not really sure what to do next. It just seems like my book, my professor, this board, and everone else I talk to you says to do something different. If it were me on my own, and I had....
(2x-1)/(x+4) + -(x+4)/x+4 I would just add the numerators to get...
(x+3) and then the denominator is (x+4) but that gives me the same wrong answer I had before. Since you mentioned the distrubutive property, maybe I multiply? (-2x^2+4)/(x+4) is the answer?

Take it easy Havyn :twisted:

Adding the denominators:
(2x - 1) + -(x + 4)
= 2x - 1 - x - 4
= x - 5

You're simply forgetting that -(a + b) = -a - b

-(3 + 8) = -11, right?
-3 - 8 = -11 ...kapish kapush :?: :idea: