Question 173555
I think you mean:  {{{((8y - 3)/(y + 7)) - ((4y - 1)/(y + 7))}}}.  Please use parentheses in the future so that it is clear what goes into your numerators and what goes into your denominators.  As written your problem could be interpreted as {{{8y - 3/y + 7 - 4y - 1/y + 7}}} which is a very different problem indeed.


Continuing with my original assumption:


{{{((8y - 3)/(y + 7)) - ((4y - 1)/(y + 7))}}}


Both fractions have the same denominator, so you can combine the numerators directly:


{{{(8y - 3-(4y-1))/(y + 7)}}}.


Eliminate the parentheses by using the distributive property:


{{{(8y - 3 - 4y + 1)/(y + 7)}}}


Combine like terms:


{{{(4y-2)/(y+7)}}}


Done.  You cannot simplify further.