Identify the restricted values and then simplify:
y^2 - 2y - 63 divided by y^2 + 4y - 21
The restricted values occur when the denominator of the fraction is equal to zero. So, we need to solve the equation y^2 + 4y - 21 = 0 to find the restricted values.
Factoring the quadratic equation, we have:
(y + 7)(y - 3) = 0
Setting each factor equal to zero, we get:
y + 7 = 0, y = -7
y - 3 = 0, y = 3
Therefore, the restricted values are y = -7 and y = 3.
Now, let's simplify the expression y^2 - 2y - 63 divided by y^2 + 4y - 21.
We can factor the numerator with the quadratic formula:
y^2 - 2y - 63 = (y - 9)(y + 7)
Again, factoring the denominator:
y^2 + 4y - 21 = (y - 3)(y + 7)
Now, we can cancel the common factors:
(y - 9)(y + 7) / (y - 3)(y + 7)
Finally, we are left with:
(y - 9) / (y - 3)