I am lost... Please help....?

Question

1. Simplify:
(x+2) over (x) over (x-2) over (3x)

2. Simplify:
(1) + (1 over 4) over (3) - (1 over 2)

Answer 1

Hi,

x+2
------
..x
=====
x-2
-----
.3x


Multiply numerator and denominator both by 3x to eliminate the little fractions.

(x+2)*3x
----------
..x
=========
(x-2)*3x
-----------
.3x

This simplifies to:

3(x+2)
---------- <==answer
x - 2


1 + ¼
--------- =
3 - ½


Making these into improper fractions and combining:

5
---
4
===
5
---
2


5........5
---.÷..---- =
4........2

5........2
---.x..---- =
4........5

10
----- = ½ <== answer
20


I hope that helps!! :-)

Answer 2

Question 1
[ (x + 2) / x ] / [ (x - 2) / 3x ]
(x + 2) (3x) / (x) (x - 2)
3 (x + 2) / (x - 2)

Question 2
1 + (1 / 4) / 3 - 1 / 2
1 + 1 / 12 - 1 / 2
12 / 12 + 1 / 12 - 6 / 12
7 / 12

Answer 3

1. [(x+2)/(x)] / [(x-2)/(3x)] --> is this what it looks like? Then,

It is the really the same as multiplying by the reciprocal -
(flip the fraction over & multiply).

(x+2)/(x) * (3x)/(x-2) -->Multiply straight across.
(3x)(x+2) / (x)(x-2) --> (num*num / denom*denom)

Reduce by what is common in both top & bottom, not in the brackets.
[3x(x+2)] / [x(x-2)] --> "x" is common, so eliminate it.

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

2. Simplify:
[(1) + (1/4)] / [(3) - (1/2)] -->Get common denominators. Everything should have 4 in the denominator.

[(4/4) + (1/4)] / [(12/4) - (2/4)] -->Do the addition/subtraction
(5/4) / (10/4) -->Now, multiply by the reciprocal.
(5/4) * (4/10) -->Multiply straight across.
(5*4) / (4*10) -->(num*num / denom*denom)
(20) / (40)

=1/2

Answer 4

I'm afraid to answer without knowing for sure how the lines look... are there any extra parenthesis or, are any of the lines longer than the others?

For instance, the answer to this...

100
---
10
--------------
2

...is 5. But if I change nothing but the length of the lines, like this:

100
--------------
10
---
2

...the answer is 20.

The first one is the same as (100/10) / 2. The second one is: 100 / (10/2).