Write each rational expression in simplest form. State all restrictions on the variables.
๐ฅ^2โ10๐ฅ/5x
To simplify the rational expression (๐ฅ^2โ10๐ฅ)/(5๐ฅ), we first factor the numerator and see if there are any common factors between the numerator and the denominator that can be canceled out.
The numerator ๐ฅ^2โ10๐ฅ can be factored as ๐ฅ(๐ฅโ10). Therefore, the rational expression becomes:
(๐ฅ^2โ10๐ฅ)/(5๐ฅ) = (๐ฅ(๐ฅโ10))/(5๐ฅ)
Now, we can cancel out the common factor of ๐ฅ between the numerator and the denominator:
(๐ฅ(๐ฅโ10))/(5๐ฅ) = (๐ฅ(๐ฅโ10))/(5) = (๐ฅโ10)/5
So, the simplified form of the rational expression is (๐ฅโ10)/5.
Now, let's state the restrictions on the variable ๐ฅ. Since the variable ๐ฅ is in the denominator of the original rational expression (5๐ฅ), the value of ๐ฅ cannot be zero. Therefore, the restriction on the variable ๐ฅ is that ๐ฅ cannot be equal to zero.