Question 315806
{{{(2/(y+4))/(3/(y-4)-1/(y^2-16))}}} Start with the given expression.




{{{(2/(y+4))/(3/(y-4)-1/((y+4)(y-4)))}}} Factor the last inner denominator.



Take note that the inner LCD is {{{(y+4)(y-4)}}}



{{{(cross((y+4))(y-4)(2/cross((y+4))))/((y+4)*cross((y-4))(3/cross((y-4)))-(cross((y+4)(y-4)))(1/(cross((y+4)(y-4)))))}}} Multiply EVERY term by the inner LCD {{{(y+4)(y-4)}}} to clear out all the inner fractions.



{{{((y-4)2)/((y+4)3-1)}}} Multiply and simplify



{{{(2(y-4))/(3(y+4)-1)}}} Rearrange the terms.



{{{(2y-8)/(3y+12-1)}}} Distribute.



{{{(2y-8)/(3y+11)}}} Combine like terms.



So {{{(2/(y+4))/(3/(y-4)-1/(y^2-16))=(2y-8)/(3y+11)}}}