Question

How do you simplify `\frac { \frac { 6} { m - n } + \frac { 6} { m } } { 2m - n }`?

Answer 1

I got `(6/(m-n)+6/m)/(2m-n) = color(red)(6/(m^2-mn))`
(...but you might want to check this)

Explanation:

`6/(m-n)+6/m`
`color(white)("XXX")=(6m+6(m-n))/((m-n)m)`

`color(white)("XXX")=(6(2m-n))/(m^2-mn)`

So
`(6/(m-n)+6/m)/(2m-n)`
`color(white)("XXX")=((6(2m-n))/(m^2-mn))/(2m-n)`

`color(white)("XXX")=(6(cancel(2m-n)))/(m^2-mn)xx1/cancel(2m-n)`

`color(white)("XXX")=6/(m^2-mn)`