To subtract these two fractions they must be over a common denominator. To create a common denominator multiply the fraction on the right by the appropriate form of #1# to not change the value of the function but to create a common denominator:
#(6y + 5)/(5y - 25) - (5/5 xx (y + 2)/(y-5)) ->#
#(6y + 5)/(5y - 25) - (5 xx (y + 2))/(5 xx (y-5)) ->#
#(6y + 5)/(5y - 25) - ((5 xx y) + (5 xx 2))/((5 xx y) - (5 xx 5)) ->#
#(6y + 5)/(5y - 25) - (5y + 10)/(5y - 25)#
We can next subtract the numerators over the common denominator:
#((6y + 5) - (5y + 10))/(5y - 25) ->#
#(6y + 5 - 5y - 10)/(5y - 25) ->#
#(6y - 5y + 5 - 10)/(5y - 25) ->#
#((6 - 5)y + (5 - 10))/(5y - 25) ->#
#(1y - 5)/(5y - 25) ->#
#(y - 5)/(5y - 25)#
We can now factor the denominator and cancel common terms:
#(y - 5)/((5 xx y) - (5 xx 5)) ->#
#(y - 5)/(5(y - 5)) ->#
#color(red)(cancel(color(black)(y - 5)))/(5color(red)(cancel(color(black)((y - 5))))) ->#
#1/5#
However, from the original expression: #(5y - 25) != 0# and #(y-5) != 0# therefore, #y != 5#