SOLUTION: simplify the complex fraction 4 ----- x+3 ----- 1/x + 3

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Question 946986: simplify the complex fraction
4
-----
x+3
-----
1/x + 3
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Pure text:
4/(x+3)/(1/x+3)

The left three curly braces, the expression, the right three curly braces:
4%2F%28x%2B3%29%2F%281%2Fx%2B3%29
The triple curly braces are the rendering tags.

I wanted to say: "Decide which is your main fraction bar to start. Suggestion is, pick the second one.", but the rendering is not letting it appear the way I want it to appear. Multiply the entire complex fraction by %28x%2Fx%29, which is useable as a lowest common denominator (for a first step).


--
That first expression is really supposed to look like this:
%284%2F%28x%2B3%29%29%2F%281%2Fx%2B3%29


Mulpiliciation by 1:

%28%284%2F%28x%2B3%29%29%2F%281%2Fx%2B3%29%29%28x%2Fx%29

%28%284x%29%2F%28x%2B3%29%29%2F%281%2B3x%29

You can formally understand the next step as multiplication by 1=%281%2F%281%2B3x%29%29%2F%281%2F%281%2B3x%29%29 which will give you, with a little adjustment, highlight_green%28%284x%29%2F%28%28x%2B3%29%283x%2B1%29%29%29; and you can then finish multiplication within the denominator.

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

simplify the complex fraction
4
-----
x+3
-----
1/x + 3
If this is: %284%2F%28x+%2B+3%29%29%2F%281%2F%28x+%2B+3%29%29? Then: 4%2F%28x+%2B+3%29%22%F7%221%2F%28x+%2B+3%29

4%2F%28x+%2B+3%29%22x%22%28x+%2B+3%29%2F1 ------ Changing DIVISION to MULTIPLICATION and INVERTING the DIVISOR

4%2Fcross%28%28x+%2B+3%29%29%22x%22cross%28%28x+%2B+3%29%29%2F1________highlight_green%284%29        

You can do the check!! 

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