Final answer:
The simplified form of the rational expression is (y-9)/(y-2), and the number that must be excluded from the domain is y=2.
Step-by-step explanation:
To simplify the rational expression (y^(2)-16y+63)/(y^(2)-9y+14), firstly we have to factorize both the numerator and the denominator. By doing this, the expression simplifies to:
[(y-7)(y-9)]/[(y-7)(y-2)]
By canceling out the common factors, we obtain:
(y-9)/(y-2)
However, we must exclude the values that would make the denominator equal to zero because division by zero is undefined. Solving the equation y-2= 0, we get the value y=2. Therefore, this number must be excluded from the domain of the simplified rational expression.
Learn more about Simplifying Rational Expressions