reduce the given rational expression to lowest terms y2 169y

reduce the given rational expression to lowest terms.
(y^2 -16)/(9y^2 -27y -36)

Solution

(y^2 -16)/(9y^2 - 27y -36)

9y^2 - 27 -36 = 9(y^2 -3y -4)

= 9( y^2-4y +y -4)

=9(y+1)(y-4)

So, (y^2 -16)/(9y^2 - 27y -36) = (y+4)(y -4)/9(y+1)(y -4)

= (y-4)/9(y+1)