#frac { 9} { y ^ { 2} - 25} - \frac { y + 7} { y ^ { 2} - 4y - 45}#
Factorising the denominators:
#(y^2-25)=(y+5)(y-5)# and
#y^2 -4y-45 = y^2 - 9y+5y-45 = y(y-9)+5(y-9) =(y+5)(y-9)#
So given expression can be written as:
#=>frac { 9} {(y-5)(y+5)} - \frac { y + 7} {(y+5)(y-9)} #
Equalising the denominators:
#=>frac { 9} {(y-5)(y+5)} xx((y-9))/((y-9))- \frac { y + 7} {(y+5)(y-9)} xx((y-5))/((y-5))#
#=>frac { 9(y-9) } {(y-5)(y+5)(y-9)}- \frac {(y+7)(y-5)} {(y+5)(y-9)(y-5)} #
#=> frac { 9(y-9)- (y+7)(y-5) } {(y-5)(y+5)(y-9)}#
#=> frac {(9y-81) - (y^2+2y -35)} {(y-5)(y+5)(y-9)}#
#=> frac {9y-81 - y^2-2y +35} {(y-5)(y+5)(y-9)}#
#=> frac {- y^2+ 7y-46} {(y-5)(y+5)(y-9)}#
