Question 186665
# 1


{{{3/(x+1)+2/(x-1)}}} Start with the given expression.



{{{(3*highlight((x-1)))/((x+1)highlight((x-1)))+2/(x-1)}}} Multiply the first fraction by {{{(x-1)/(x-1)}}}



{{{(3x-3)/((x+1)(x-1))+2/(x-1)}}} Distribute



{{{(3x-3)/((x+1)(x-1))+(2*highlight((x+1)))/(highlight((x+1))(x-1))}}} Multiply the second fraction by {{{(x+1)/(x+1)}}}



{{{(3x-3)/((x+1)(x-1))+(2x+2)/((x+1)(x-1))}}} Distribute



{{{(3x-3+2x+2)/((x+1)(x-1))}}} Combine the fractions.



{{{(5x-1)/((x+1)(x-1))}}} Combine like terms.



So {{{3/(x+1)+2/(x-1)=(5x-1)/((x+1)(x-1))}}} where {{{x<>1}}} or {{{x<>-1}}}



---------------------------------------------------------------


# 2


{{{(1/9+1/(3x))(x/9-1/x)}}} Start with the given expression.



{{{(1/9)(x/9)+(1/9)(-1/x)+(1/(3x))(x/9)+(1/(3x))(-1/x)}}} FOIL the expression



Note: use the formula {{{(A+B)(C+D)=(A)(C)+(A)(D)+(B)(C)+(B)(D)}}} to FOIL



{{{x/81-1/(9x)+1/27-1/(3x^2)}}} Multiply



So {{{(1/9+1/(3x))(x/9-1/x)=x/81-1/(9x)+1/27-1/(3x^2)}}}