SOLUTION: I am a homeschooling mom. I have come across these problems. I don't understand how it works. I want to be able to understand in order to teach my kid the right way. Here are t

Question 128130: I am a homeschooling mom. I have come across these problems. I don't understand how it works. I want to be able to understand in order to teach my kid the right way.
Here are the problems in one 'sentence': ( if you see the dashes between these numbers - that is division. And..as for the # 3 and # 4 ...I have been unable to get the denominator to look the way it should... under the first combination it is divided by 2x; and the second combination, it is divded by an x.

1.
3/2 + 3/x
--------- =
2+4/x

2.
(3/2+3/x)/(2+4/x)=

3.
(3x+6)/(2x+4)
----- ---- =
2x x

4.
3x+6 * 2x+4
---- ---- =
2x x

5.

-----------

I would very much appreciate your explanation and how you arrive to the answer..and please make it in layman's terms. Thanks.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
1.
+
-------
2 +
:
Put the fractions in the numerator & denominator over a single common denominator

----------

:
Factor out 3 in the numerator & 2 in the denominator

----------

;
Remember when you divide fractions, invert the dividing fraction and multiply
*
:
Cancel out (x+2) and x, leaving
* =
:
:
2.
This is the same as the first one
:
3. This is similar to the first equation after we put it over common denominators

----------

:
Factor out 3 in the numerator & 2 in the denominator

----------

;
Remember when you divide fractions, invert the dividing fraction and multiply
*
:
Cancel out (x+2) and x, leaving
* =
:
:
5.
6x^2+24x+24
-----------
2x^2
:
notice that you can factor out 6 in the numerator, then cancel 2 into 6
=
:
The numerator has a perfect square and can be factored to:
=

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