SOLUTION: Please help me with this problem. I am confused and am trying to learn how to solve this type of problem. It is a fraction on top of a fraction and needs to be simplified; If anyon

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Please help me with this problem. I am confused and am trying to learn how to solve this type of problem. It is a fraction on top of a fraction and needs to be simplified; If anyon      Log On


   

Question 188737: Please help me with this problem. I am confused and am trying to learn how to solve this type of problem. It is a fraction on top of a fraction and needs to be simplified; If anyone can help me understand this I would greatly appreciate it. Thank you.

2
--- +1
x+3
---
4
---- +2
x+3
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%282%2F%28x%2B3%29%2B1%29%2F%284%2F%28x%2B3%29%2B2%29 Start with the given expression.


%282%2F%28x%2B3%29%2B%28x%2B3%29%2F%28x%2B3%29%29%2F%284%2F%28x%2B3%29%2B2%29 Multiply the term "1" in the numerator by %28x%2B3%29%2F%28x%2B3%29


%28%282%2Bx%2B3%29%2F%28x%2B3%29%29%2F%284%2F%28x%2B3%29%2B2%29 Combine the upper fractions.


%28%28x%2B5%29%2F%28x%2B3%29%29%2F%284%2F%28x%2B3%29%2B2%29 Combine like terms.


%28%28x%2B5%29%2F%28x%2B3%29%29%2F%284%2F%28x%2B3%29%2B%282%28x%2B3%29%29%2F%28x%2B3%29%29 Multiply the term "2" in the denominator by %28x%2B3%29%2F%28x%2B3%29


%28%28x%2B5%29%2F%28x%2B3%29%29%2F%284%2F%28x%2B3%29%2B%282x%2B6%29%2F%28x%2B3%29%29 Distribute


%28%28x%2B5%29%2F%28x%2B3%29%29%2F%28%284%2B2x%2B6%29%2F%28x%2B3%29%29 Combine the lower fractions.


%28%28x%2B5%29%2F%28x%2B3%29%29%2F%28%282x%2B10%29%2F%28x%2B3%29%29 Combine like terms.


%28%28x%2B5%29%2F%28x%2B3%29%29%2A%28%28x%2B3%29%2F%282x%2B10%29%29 Multiply the upper fraction by the reciprocal of the lower fraction.


%28%28x%2B5%29%2F%28x%2B3%29%29%2A%28%28x%2B3%29%2F%282%28x%2B5%29%29%29 Factor 2x%2B10 to get 2%28x%2B5%29


%28%28x%2B5%29%28x%2B3%29%29%2F%282%28x%2B3%29%28x%2B5%29%29%29 Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


1%2F2 Simplify


So %282%2F%28x%2B3%29%2B1%29%2F%284%2F%28x%2B3%29%2B2%29 simplifies to 1%2F2


In other words, %282%2F%28x%2B3%29%2B1%29%2F%284%2F%28x%2B3%29%2B2%29=1%2F2 where x%3C%3E-5 or x%3C%3E-3



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Note: in this case, the problem can be simplified in another way:


%282%2F%28x%2B3%29%2B1%29%2F%284%2F%28x%2B3%29%2B2%29 Start with the given expression.


%282%2F%28x%2B3%29%2B1%29%2F%282%282%2F%28x%2B3%29%2B1%29%29 Factor out the GCF 2 from the denominator


highlight%282%2F%28x%2B3%29%2B1%29%2F%282%2Ahighlight%28%282%2F%28x%2B3%29%2B1%29%29%29 Highlight the common terms.


cross%282%2F%28x%2B3%29%2B1%29%2F%282%2Across%28%282%2F%28x%2B3%29%2B1%29%29%29 Cancel out the common terms.


1%2F2 Simplify


So %282%2F%28x%2B3%29%2B1%29%2F%284%2F%28x%2B3%29%2B2%29=1%2F2 where x%3C%3E-5 or x%3C%3E-3


Note: this technique does not always apply.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
----------
[(2/(x+3))+1] / [(4/(x+3)) +2]
-----------
[2 + x+3]/(x+3) / [4 + 2(x+3)]/(x+3
-------------
Invert and multiply
[[2 + x+3]/(x+3)]
------
Simplify and cancel to get:
= [x+5] /[2x +10]
-----
Factor:
= [x+5] / [2(x+5)]
---
Cancel to get:
= 1/2
==================================
Cheers,
Stan H.