SOLUTION: simplify the complex fraction, reduce to lowest terms {{{matrix(3,1,1/9 + 1/(3x),"---------",x/9 - 1/x)}}}

Algebra ->  Rational-functions -> SOLUTION: simplify the complex fraction, reduce to lowest terms {{{matrix(3,1,1/9 + 1/(3x),"---------",x/9 - 1/x)}}}      Log On


   

Question 174645: simplify the complex fraction, reduce to lowest terms
matrix%283%2C1%2C1%2F9+%2B+1%2F%283x%29%2C%22---------%22%2Cx%2F9+-+1%2Fx%29
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
matrix%283%2C1%2C1%2F9+%2B+1%2F%283x%29%2C%22---------%22%2Cx%2F9+-+1%2Fx%29

Put parentheses around numerator and denominator:
matrix%283%2C1%2C%281%2F9+%2B+1%2F%283x%29%29%2C%22---------%22%2C%28x%2F9+-+1%2Fx%29%29

The LCD of all the denominators is 9x, so we
multiply by %289x%29%2F%289x%29 but we first write it as

matrix%283%2C1%2C%28%289x%29%2F1%29%2C%22---------%22%2C%28%289x%29%2F1%29%29 

so everything will be fractions:



Now we indicate the multiplication of numerators 
and denominators:



Now we distribute:



Now we cancel:
             3


All that's left is

%28x%2B3%29%2F%28x%5E2-9%29

Factor the denominator:

%28x%2B3%29%2F%28%28x-3%29%28x%2B3%29%29

Cancel the %28x%2B3%29's

matrix%282%2C1%2C1%2C+%28cross%28x%2B3%29%29%2F%28%28x-3%29%28cross%28x%2B3%29%29%29%29

Now all that's left is

1%2F%28x-3%29

Edwin