Question

how do you simplify this:
\[x ^{-1}+y ^{-1} \over (x+y)^{-1}\]

Answer 1

((1/x)+(1/y))/(1/(x+y)), right?
((y/xy)+(x/xy))*(x+y)
((x+y)/xy)*(x+y)
(x+y)^2/xy
1/y+2+1/x

Answer 2

where did you get the *(x+y)??

Answer 3

dividing by a fraction is the same as multiplying its inverse. Put mathematically, \[(1/x)^-1=x\]

Answer 4

ok!! would you know how to simplify this one also?

http://openstudy.com/groups/mathematics#/groups/mathematics/updates/4e3b74ee0b8b269281820dd8