Write the rational expression in lowest terms
xm-xn-4m+4n/ xm-xn+4m-4n
MULTIPLE CHOICE
a) x-4/x+4
b) x+4/x-4
c) m-n/m+n
d) m+n/m-n
First: let's factor the numerator: xm - xn - 4m + 4n
xm - xn - (4m - 4n)
x(m - n) - 4(m - n)
(m - n)(x - 4)
Then: let's factor the denominator: xm - xn + 4m - 4n
x(m - n) + 4(m - n)
(m - n)(x + 4)
Putting the two together: [ (m - n)(x - 4) ] / [ (m - n)(x + 4) ]
(m - n) is a common factor in both the numerator and the denominator; cancel it ...
leaving us with: (x - 4) / (x + 4)