Question

Simplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression.
y^2+6y-16/y^2+2y-48

Answer 1

To simplify the rational expression (y^2 + 6y - 16)/(y^2 + 2y - 48), we first factor the numerator and denominator:

Numerator: y^2 + 6y - 16 = (y + 8)(y - 2)
Denominator: y^2 + 2y - 48 = (y + 8)(y - 6)

Now, we can rewrite the expression as ((y + 8)(y - 2))/((y + 8)(y - 6)).

Next, we can simplify the expression by canceling out the common factors:
((y - 2)/(y - 6))

The numbers that must be excluded from the domain of the simplified rational expression are the values of y that make the denominator zero, since division by zero is undefined. In this case, y = 6 is the value that makes the denominator zero, so y = 6 must be excluded from the domain.