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

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> 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      Log On


   



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.
+6x%5E2%2B24x%2B24+
-----------
+2x%5E2+

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) About Me  (Show Source):
You can put this solution on YOUR website!
1.
3%2F2 + 3%2Fx
-------
2 + 4%2Fx
:
Put the fractions in the numerator & denominator over a single common denominator
%28%283x+%2B+2%283%29%29%29%2F%282x%29
----------
%28%282x+%2B+4%29%29%2Fx
:
%28%283x+%2B+6%29%29%2F%282x%29
----------
%28%282x+%2B+4%29%29%2Fx
:
Factor out 3 in the numerator & 2 in the denominator
%283%28x+%2B+2%29%29%2F%282x%29
----------
%282%28x+%2B+2%29%29%2Fx
;
Remember when you divide fractions, invert the dividing fraction and multiply
%283%28x%2B2%29%29%2F%282x%29 * x%2F%282%28x%2B2%29%29
:
Cancel out (x+2) and x, leaving
3%2F2 * 1%2F2 = 3%2F4
:
:
2.
This is the same as the first one
:
3. This is similar to the first equation after we put it over common denominators
%28%283x%2B6%29%29%2F%282x%29
----------
%28%282x%2B4%29%29%2Fx
:
Factor out 3 in the numerator & 2 in the denominator
%283%28x+%2B+2%29%29%2F%282x%29
----------
%282%28x+%2B+2%29%29%2Fx
;
Remember when you divide fractions, invert the dividing fraction and multiply
%283%28x%2B2%29%29%2F%282x%29 * x%2F%282%28x%2B2%29%29
:
Cancel out (x+2) and x, leaving
3%2F2 * 1%2F2 = 3%2F4
:
:
5.
6x^2+24x+24
-----------
2x^2
:
notice that you can factor out 6 in the numerator, then cancel 2 into 6
%286%28x%5E2+%2B+4x+%2B+4%29%29%2F%282x%5E2%29 = %283%28x%5E2+%2B+4x+%2B+4%29%29%2F%28x%5E2%29
:
The numerator has a perfect square and can be factored to:
%283%28x%2B2%29%28x%2B2%29%29%2F%28x%5E2%29 = %283%28x%2B2%29%5E2%29%2F%28x%5E2%29