SOLUTION: I need help on two(2) problems; Please!! they are (3/x+1)+(2/x-1)= and the next one is (1/9+1/3x)(x/9-1/x)=

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need help on two(2) problems; Please!! they are (3/x+1)+(2/x-1)= and the next one is (1/9+1/3x)(x/9-1/x)=      Log On


   

Question 186665: I need help on two(2) problems; Please!! they are (3/x+1)+(2/x-1)= and the next one is (1/9+1/3x)(x/9-1/x)=
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

3%2F%28x%2B1%29%2B2%2F%28x-1%29 Start with the given expression.


Multiply the first fraction by %28x-1%29%2F%28x-1%29


%283x-3%29%2F%28%28x%2B1%29%28x-1%29%29%2B2%2F%28x-1%29 Distribute


Multiply the second fraction by %28x%2B1%29%2F%28x%2B1%29


%283x-3%29%2F%28%28x%2B1%29%28x-1%29%29%2B%282x%2B2%29%2F%28%28x%2B1%29%28x-1%29%29 Distribute


%283x-3%2B2x%2B2%29%2F%28%28x%2B1%29%28x-1%29%29 Combine the fractions.


%285x-1%29%2F%28%28x%2B1%29%28x-1%29%29 Combine like terms.


So 3%2F%28x%2B1%29%2B2%2F%28x-1%29=%285x-1%29%2F%28%28x%2B1%29%28x-1%29%29 where x%3C%3E1 or x%3C%3E-1


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# 2

%281%2F9%2B1%2F%283x%29%29%28x%2F9-1%2Fx%29 Start with the given expression.


FOIL the expression


Note: use the formula %28A%2BB%29%28C%2BD%29=%28A%29%28C%29%2B%28A%29%28D%29%2B%28B%29%28C%29%2B%28B%29%28D%29 to FOIL


x%2F81-1%2F%289x%29%2B1%2F27-1%2F%283x%5E2%29 Multiply


So %281%2F9%2B1%2F%283x%29%29%28x%2F9-1%2Fx%29=x%2F81-1%2F%289x%29%2B1%2F27-1%2F%283x%5E2%29