Expressing as a single fraction

[Theinvoker]

Hiya,

Just found the forums and loving them so far, going to spend some time tomorrow trauling through some of the interesting discusssions I've seen.
I am starting a course soon and have been going over some maths problems to prepare, however there is one that I never used to be able to figure out and turns out i still can't lol It's todo with adding fractions with more than 2 parts.

The practice question I have here is:

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

I can see without too much trouble that the common denominator is 2(x+4)^2 but the closest I have got to the correct answer is x^2+x+25 / 2(x+4)^2 and according to the answers its slightly wrong.

I am fine when it's just 2 fractions to be added but can't understand how you get the answer when its 3 or more.

If anyone could help explain it would be most appreciated :)

Regards,

Theinvoker

 

[Dick]

For 1/(2(x+4)) (I assume that's what you mean, you should use more parentheses), multiply top and bottom by (x+4) for the second term multiply top and bottom by 2 and for the last one by (x+4)^2. Now they are all over your common denominator. What's the sum of the numerators?

 

[real10]

Hiya,

Just found the forums and loving them so far, going to spend some time tomorrow trauling through some of the interesting discusssions I've seen.
I am starting a course soon and have been going over some maths problems to prepare, however there is one that I never used to be able to figure out and turns out i still can't lol It's todo with adding fractions with more than 2 parts.

The practice question I have here is:

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

I can see without too much trouble that the common denominator is 2(x+4)^2 but the closest I have got to the correct answer is x^2+x+25 / 2(x+4)^2 and according to the answers its slightly wrong.

I am fine when it's just 2 fractions to be added but can't understand how you get the answer when its 3 or more.

If anyone could help explain it would be most appreciated :)

Regards,

Theinvoker

$$\frac{a}{u}+\frac{b}{v}+\frac{c}{w}=\frac{v*w*a+u*w*b+u*v*c}{u*v*w}$$
follow the pattern generalizing it further to n fractions...

in ur specific case v = u^2 which leads to simplifcations but the formula above would help if in the general sense..

 

[Dick]

Forget the formula. You got the common denominator. That's half the battle. Now multiply top and bottom of each fraction by what's lacking from the common denominator. Formula? Jeez.

 

[real10]

Forget the formula. You got the common denominator. That's half the battle. Now multiply top and bottom of each fraction by what's lacking from the common denominator. Formula? Jeez.

I thought the original poster wanted to understand how to add/sub for more than 2 fractions...

I am fine when it's just 2 fractions to be added but can't understand how you get the answer when its 3 or more.

 

[Dick]

I suspect the poster has already memorized a formula for two fractions. I wouldn't give the OP a formula for three. The procedure for adding doesn't depend on a formula. Just a pedagogical notion. Sorry if I seemed dismissive of your contribution.

 

[real10]

I suspect the poster has already memorized a formula for two fractions. I wouldn't give the OP a formula for three. The procedure for adding doesn't depend on a formula. Just a pedagogical notion. Sorry if I seemed dismissive of your contribution.

the procedure works for fraction addition and makes sense,doesnt it??

 

[Dick]

What procedure? Finding a common denominator and learning how to use it makes sense.

 

[HallsofIvy]

The point is, do you really think it is a good thing for someone to memorize a formula for adding two fractions, a different formula for adding three, fractions, still a different formula for adding four fractions, ... ? Far better to understand that once you have changed each fraction, no matter how many there are, to the common denominator, you just add the numerators.

 

[Theinvoker]

Thanks for all the help. I thought I had it so I went back to the question and followed what was said, but I still get the wrong answer :(

My workings:

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

1(x+4) + 6 + 1(x+4)^2 / 2(x+4)^2 =

x^2 + x + 26 / 2(x+4)^2

I've been over it and over it and all seems to be right, but the answer in the book is x^2 + 9x + 26 / 2(x+4)^2 and I can't see where you get 9x from for the life of me lol.

Thanks again.

 

[Dick]

Use more parentheses. 1+2/1 can be either 3/2, (1+2)/1 or 3, 1+(2/1). You might know what you mean but somebody else might not. That said, your problem is that (x+4)^2 is not equal to x^2+4^2. (1+4)^2=5^2=25. 1^2+4^2=17. They aren't the same. What went wrong?

 

[Theinvoker]

1(x+4)^2 = (x+4)(x+4) = x^2 + 8x +16 add that to the rest and you get the right answer! Yay! :)

Thank you very much! If it had been explained to me like that 10 years ago I might have got it sooner (except the last (x+4)^2 bit that as me being a plonker hehe).

Thanks again for all the help, sure Ill be back again when the course starts if not before, and once I start picking up new knowledge off it, help others out that are where i am now :)