Write each rational expression in simplest form. State all restrictions on the variables.
4๐ฅ^2+5๐ฅโ6/๐ฅ^2โ6๐ฅโ16
To simplify the rational expression 4๐ฅ^2 + 5๐ฅ - 6 / ๐ฅ^2 - 6๐ฅ - 16, we can factor both the numerator and denominator.
The numerator factors as: (4๐ฅ - 3)(๐ฅ + 2)
The denominator factors as: (๐ฅ - 8)(๐ฅ + 2)
Cancel out the common factor of (๐ฅ + 2) from both the numerator and denominator:
(4๐ฅ - 3)(๐ฅ + 2) / (๐ฅ - 8)(๐ฅ + 2) = (4๐ฅ - 3) / (๐ฅ - 8)
The expression simplifies to (4๐ฅ - 3) / (๐ฅ - 8) in its simplest form.
Restrictions on the variable: The expression is undefined when the denominator (๐ฅ - 8) is equal to zero. Therefore, ๐ฅ cannot be equal to 8.