Question 126340
{{{(2+x)/x^2+(x-3)/3x}}}


You would have had an easier time of it had you chosen the LOWEST common denominator, {{{3x^2}}} rather than using the simple product of the denominators {{{3x^3}}}.


However, you have done everything else correctly, except for taking the final step.


Your answer {{{(x^3+6x)/3x^3}}}, can be rewritten by factoring as:
{{{(x(x^2+6))/(x(3x^2))}}}.  Then divide out the common factor:


{{{(cross(x)(x^2+6))/(cross(x)(3x^2))}}}


{{{(x^2+6)/(3x^2)}}}, which is the answer from the book.  Technically, your answer was correct, it just wasn't reduced to lowest terms.