SOLUTION: Adding Rational Expressions Please walk me thru each step, but especially involving the LCD: Add: {{{3/(x^3-x)}}}{{{""+""}}}{{{4/(x^2+2x+1)}}}

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Question 390385: Adding Rational Expressions
Please walk me thru each step, but especially involving the LCD:
Add:


Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
Add:


Factor the first denominator completely:



Factor the second denominator completely:





Creating the LCD:

Rule:
The LCD must contain each factor of each denominator to the largest power
it appears in any denominator.

The factor  occurs to the first power in the first fraction,
and not at all in the second fraction, so the LCD will contain 
to the first power.

The factor  occurs to the first power in the first fraction,
and not at all in the second fraction, so the LCD will contain 
to the first power.

The factor  occurs to the first power in the first fraction,
and to the 2nd power in the second fraction, so the LCD will contain 
 to the 2nd power, or 

Therefore the LCD = 



The first fraction needs to be multiplied by  so that
its denominator will become the LCD:




The second fraction needs to be multiplied by 
so that its denominator will also become the LCD:








Multiply the numerators out but do not multiply the
denominators out.



Combine the numerators over the LCD:





The numerator doesn't factor, so we leave it like that.

Edwin




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