the least common denominator is (y-7) (y+7) (y-1)
y/y^2-49 and y/y^2+6y-7
We can factor the first denominator into
y^2-49 = (y-7) (y+7) by using the difference of squares
(a^2-b^2) = (a-b)(a+b)
We can factor the second denominator into
y^2+6y-7 = (y+7)(y-1) by factoring.
What two terms multiply to -7 and add to -6
7*-1 = -7
7-1 =6
(y+7)(y-1)
We need to take the greatest number from either each term
The first term has (y-7) (y+7)
The second term has (y+7)(y-1)
We have one (y-7) in each term
We have one (y+7) in each term
We have one (y-1) in each term
(y-7) (y+7) (y-1)