Please tell me how to simplify this problem...?

Question

Simplify
3+3/
3+3/
3+3/x
This problem was hard to write numerically, but all in all the question is asking 3+3 divided by 3+3divided by 3+3 divided by x. Please help me.

Answer 1

(3+3)/(3+3)/(3+3)/x

simplify the top 6/6 = 1
simplify the bottom 6/x
so (1/6)/x

Answer 2

My result: it's 3 (5 x + 4) / (4 x + 3).

I think that you are asking us to evaluate what is called a "continued fraction," and that other responders have simply missed that point.

Strange as it may seem, it is sometimes harder to evaluate a FINITE continued fraction (one that stops at some point), than an INFINITELY continued fraction (never ends!) with some logical pattern to all the terms.

In the present case, I'm afraid that there's nothing to do but grit your teeth and work it out.

Write out the complete continued fraction. As you said, it's very hard to show it in this present "Answers" format. You start by working out what's going on at the LEAST significant end of the whole continued fraction, down there under the second horizontal line. You simplify what you can there; then you move up to the next level and do the same again. With a longer continued fraction, you'd have to keep working successively upWards through more and more levels. Let's isllustrate the general such process with your specific example :

At the "almost deepest level" (under the second horizontal line), you'll see ' 3 + 3 / x .' Those 3's will cancel against the 3 above the line. Multiplying top and bottom by x, you'll now see x / (x + 1) there.

So, under the first horizontal line you now have 3 + x / (x + 1). Multiply top and bottom by (x + 1), giving you 3 (x + 1) / [3(x + 1) + x]
= 3 (x + 1) / (4 x + 3).

You now have simply 3 + 3 (x + 1) / (4 x + 3). You can now combine all that together to give you:

3 (5 x + 4) / (4 x + 3).

It was rather tedious to do this, but I think that the point of the problem was to show that if you set up a logical method starting from the deepest "end" of the fraction, you can dig yourself out of the fractional hole and emerge into the broad sunlight of a new day!

Live long and prosper.

Answer 3

You still aren't quite clear. It could be asked two ways so I'll address both.
1) if it's (3+3)/(3+3)/(3+3)/x
follow order of operations:
there aren't any exponents, so move on to parenthesis
solve all the stuff inside parenthesis
(3+3)=6>>>>rewrite the problem: 6/6/6/x
now multiply & divide going from left to right. there aren't any multiplications to do so just go through
6/6=1>>>>rewrite the problem: 1/6/x
1/6~.1666>>>>rewrite the problem: .1666/x
next you would add or subtract, but there is none of that to do.
this is the most it can be simplified
2)this assumes it is as it is written 3+3/3+3/3+3/x
This way is slightly more difficult, but approach it the same way
Exponents(none) and parenthesis(none) first
multiply(none) and divide
3/3=1>>>> rewrite the problem: 3+1+1+3/x
3/x can't be simplified
now add and subtract(none)
so you get 5+3/x.
I don't know what grade you're in so I'm not sure if it would be expected for you to go this far, but now you need to get a common denominator(bottom of the fraction). It's easy in this case since the two denominators are 1 & x>>> it's x
multiply 5 by x/x(this equals 1, so you aren't technically changing the numbers)>>>rewrite: (5x/x)+(3/x)
you can add numbers with like denominators so add the numerators(top of the fraction) and leave the denominators the same.
5x+3 is the most you can do>>>>your final simplified answer is (5x+3)/x
hope this helps

Answer 4

Unforutnally they are all wrong. You must look what they are asking and follow the rules of math. 3 + 3/3 + 3/3 + 3/x. Now you have 3 + 1 + 1 + 3/x. Which simplifies to 5 + 3/x.

Answer 5

the first two cancel each other out. it's 3+3 divided by x... 6/x

Answer 6

Just multiply the number outside the parenthesis with the number inside the parenthesis. 1. 5 x 3 =15, 5 x -x= -5x 15-5x 2. -2 x 6 = -12 3. x x x= x^2, x x -4= -4x x^2-4x 4. 2x x x=2x^2, 2x x 4=8x 2x^2+8x

Answer 7

the answer is:

6 / 6 / 6 / x
6 divided by 6 (a number divided by itself is always one)...so its one

= 1 / x

Answer 8

6/x because 3+3/3+3/3+3/x=6/6/6/x=6/6x/6=6/x

Answer 9

It should just be 1/x as long as the problem isn't solving for x

Answer 10

(1/6)/x