(y+2 ) (y)

--------- subtract -----------
(y^2-49) (y^2-6y+7)

The directions are subtract and simplify....

(y+2)y = y^2+2y.

y^2+2y-(y^2-49)(y^2-6y+7) =
y^2+2y-(y^4-6y^3+7y^2-49y^2+294y-343)=y^2+2y-y^4+6y^3-7y^2+49y^2-294y+343=
-y^4+6y^3+43y^2-292y+343.

To subtract and simplify the given expression, you need to find a common denominator for both fractions. Let's break down the steps:

Step 1: Factor the denominators
The first denominator, y^2 - 49, can be factored using the difference of squares formula: (y - 7)(y + 7).
The second denominator, y^2 - 6y + 7, cannot be factored any further.

Step 2: Find the least common denominator (LCD)
The LCD is the least common multiple of the factors of both denominators. In this case, the LCD is (y - 7)(y + 7)(y^2 - 6y + 7).

Step 3: Rewrite the fractions using the LCD
For the first fraction, multiply both the numerator and denominator by (y - 7)(y^2 - 6y + 7).
For the second fraction, multiply both the numerator and denominator by (y + 7)(y^2 - 49).

After multiplying, the expression becomes:

(y + 2)(y - 7)(y^2 - 6y + 7) - y(y + 7)(y^2 - 49)
------------------------------------------------------------------
(y^2 - 49)(y^2 - 6y + 7)

Step 4: Simplify the expression
Distribute and simplify each term in the expression:

(y^3 - 5y^2 - 47y + 14) - (y^4 - 42y - 49y^2 + 2058)
----------------------------------------------------------
(y^4 - 6y^3 + 7y^2 - 49y^2 + 294y - 343)

Combine like terms:

- y^4 + 6y^3 + 56y^2 - 337y + 14
-------------------------------
y^4 - 56y^2 + 294y - 343

Thus, the simplified expression is (- y^4 + 6y^3 + 56y^2 - 337y + 14) divided by (y^4 - 56y^2 + 294y - 343).