Question

[(y+4)/(y+7)]+1=(y+3)/(y+1)

Answer 1

First note that y cannot equal -7 or -1 as division by zero is undefined.  So that if it comes up in our solution we know that it is not a real solution.

[(y+4)/(y+7)]+1=(y+3)/(y+1)  make the left side have a common denominator

(y+4+y+7)/(y+7)=(y+3)/(y+1)  combine like terms on left side

(2y+11)/(y+7)=(y+3)/(y+1)  cross multiply 

(2y+11)(y+1)=(y+3)(y+7)  expand

2y^2+13y+11=y^2+10y+21  subtract y^2 from both sides

y^2+13y+11=10y+21  subtract 10y from both sides

y^2+3y+11=21 subtract 21 from both sides

y^2+3y-10=0  expand so factoring is easier

y^2-2y+5y-10=0  factor

y(y-2)+5(y-2)=0  which is equal to

(y+5)(y-2)=0

y=-5 or 2