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)}}}

Algebra ->  Polynomials-and-rational-expressions -> 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)}}}       Log On


   

Question 390385: Adding Rational Expressions
Please walk me thru each step, but especially involving the LCD:
Add:
3%2F%28x%5E3-x%29%22%22%2B%22%224%2F%28x%5E2%2B2x%2B1%29
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Add:
3%2F%28x%5E3-x%29%22%22%2B%22%224%2F%28x%5E2%2B2x%2B1%29

Factor the first denominator completely:

x%5E3-x%22%22=%22%22x%28x%5E2-1%29%22%22=%22%22x%28x-1%29%28x%2B1%29

Factor the second denominator completely:

x%5E2%2B2x%2B1%22%22=%22%22%28x%2B1%29%28x%2B1%29%22%22=%22%22%28x%2B1%29%5E2

3%2F%28x%28x-1%29%28x%2B1%29%29%22%22%2B%22%224%2F%28x%2B1%29%5E2

Creating the LCD:

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

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

The factor %28x-1%29 occurs to the first power in the first fraction,
and not at all in the second fraction, so the LCD will contain %28x-1%29
to the first power.

The factor %28x%2B1%29 occurs to the first power in the first fraction,
and to the 2nd power in the second fraction, so the LCD will contain 
%28x%2B1%29 to the 2nd power, or %28x%2B1%29%5E2

Therefore the LCD = x%28x-1%29%28x%2B1%29%5E2

3%2F%28x%28x-1%29%28x%2B1%29%29%22%22%2B%22%224%2F%28x%2B1%29%5E2

The first fraction needs to be multiplied by red%28%28%28x%2B1%29%29%2F%28%28x%2B1%29%29%29 so that
its denominator will become the LCD:

%22%22%2B%22%224%2F%28x%2B1%29%5E2


The second fraction needs to be multiplied by red%28++%28x%28x-1%29%29%2F%28x%28x-1%29%29++%29
so that its denominator will also become the LCD:



%22%22%2B%22%22


++%283%28x%2B1%29%29%2F%28x%28x-1%29%28x%2B1%29%5E2%29%22%22%2B%22%22%284x%28x-1%29%29%2F%28x%28x-1%29%28x%2B1%29%5E2%29

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

++%283x%2B3%29%2F%28x%28x-1%29%28x%2B1%29%5E2%29%22%22%2B%22%22%284x%5E2-4x%29%2F%28x%28x-1%29%28x%2B1%29%5E2%29

Combine the numerators over the LCD:

%283x%2B3%2B4x%5E2-4x%29%2F%28x%28x-1%29%28x%2B1%29%5E2%29

%284x%5E2-x%2B3%29%2F%28x%28x-1%29%28x%2B1%29%5E2%29

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

Edwin