SOLUTION: {{{(3x^3)/(x^3+27) - x/(x+3) + (2x^2)/(x^2-3x+9)}}}

Algebra ->  Algebra  -> Exponents-negative-and-fractional -> SOLUTION: {{{(3x^3)/(x^3+27) - x/(x+3) + (2x^2)/(x^2-3x+9)}}}      Log On

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Question 103968: %283x%5E3%29%2F%28x%5E3%2B27%29+-+x%2F%28x%2B3%29+%2B+%282x%5E2%29%2F%28x%5E2-3x%2B9%29
Answer by jim_thompson5910(14853) About Me  (Show Source):
You can put this solution on YOUR website!
%283x%5E3%29%2F%28x%5E3%2B27%29+-+x%2F%28x%2B3%29+%2B+%282x%5E2%29%2F%28x%5E2-3x%2B9%29 Start with the given expression



%283x%5E3%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29+-+x%2F%28x%2B3%29+%2B+%282x%5E2%29%2F%28x%5E2-3x%2B9%29 Factor x%5E3%2B27 into %28x%2B3%29%28x%5E2-3x%2B9%29



So this means the LCM is %28x%2B3%29%28x%5E2-3x%2B9%29 (since every denominator has either x%2B3, x%5E2-3x%2B9, or both). So we want every fraction to have a denominator of %28x%2B3%29%28x%5E2-3x%2B9%29



%283x%5E3%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29+-+%28%28x%5E2-3x%2B9%29%2F%28x%5E2-3x%2B9%29%29%28x%2F%28x%2B3%29%29+%2B+%282x%5E2%29%2F%28x%5E2-3x%2B9%29 Multiply the second fraction by %28x%5E2-3x%2B9%29%2F%28x%5E2-3x%2B9%29


%283x%5E3%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29+-+x%28x%5E2-3x%2B9%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29%2B+%282x%5E2%29%2F%28x%5E2-3x%2B9%29 Multiply


%283x%5E3%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29+-+%28x%5E3-3x%5E2%2B9x%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29%2B+%282x%5E2%29%2F%28x%5E2-3x%2B9%29 Distribute



%283x%5E3%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29+-+%28x%5E3-3x%5E2%2B9x%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29%2B+%28%28x%2B3%29%2F%28x%2B3%29%29%28%282x%5E2%29%2F%28x%5E2-3x%2B9%29%29 Multiply the third fraction by %28x%2B3%29%2F%28x%2B3%29


%283x%5E3%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29+-+%28x%5E3-3x%5E2%2B9x%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29%2B+%282x%5E2%29%28x%2B3%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29 Multiply



%283x%5E3%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29+-+%28x%5E3-3x%5E2%2B9x%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29%2B+%0D%0A%282x%5E3%2B6x%5E2%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29 Distribute

Since we have a common denominator, we can combine the fractions

%283x%5E3-+%28x%5E3-3x%5E2%2B9x%29%2B2x%5E3%2B6x%5E2%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29+ Combine the fractions


%283x%5E3-x%5E3%2B3x%5E2-9x%2B2x%5E3%2B6x%5E2%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29+ Distribute the negative


%284x%5E3%2B9x%5E2-9x%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29+ Combine like terms



%28%28x%2B3%29%284x%5E2-3x%29%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29+ Factor the numerator


%28cross%28%28x%2B3%29%29%284x%5E2-3x%29%29%2F%28cross%28%28x%2B3%29%29%28x%5E2-3x%2B9%29%29+ Cancel like terms



%284x%5E2-3x%29%2F%28x%5E2-3x%2B9%29+ Simplify


%28x%284x-3%29%29%2F%28x%5E2-3x%2B9%29+ Factor out an x



So %283x%5E3%29%2F%28x%5E3%2B27%29+-+x%2F%28x%2B3%29+%2B+%282x%5E2%29%2F%28x%5E2-3x%2B9%29 simplifies to %28x%284x-3%29%29%2F%28x%5E2-3x%2B9%29+