Write each rational expression in simplest form. State all restrictions on the variables
2๐ฅ^2โ2๐ฅโ12/4๐ฅโ12
To simplify the rational expression, we can start by factoring the numerator and denominator if possible.
The numerator is 2๐ฅ^2โ2๐ฅโ12. We can factor out a 2 from each term, which gives us 2(๐ฅ^2โ๐ฅโ6). Now we need to factor the quadratic expression ๐ฅ^2โ๐ฅโ6. This can be factored as (๐ฅโ3)(๐ฅ+2).
So the numerator can be written as 2(๐ฅโ3)(๐ฅ+2).
The denominator is 4๐ฅโ12 which can be factored out a common factor of 4, giving us 4(๐ฅโ3).
Now, we can cancel out the common factor of (๐ฅโ3) in the numerator and denominator:
2(๐ฅโ3)(๐ฅ+2)/4(๐ฅโ3)
Canceling out the common factor, we are left with:
2(๐ฅ+2)/4
Now we can simplify further. We can simplify the expression 2(๐ฅ+2) by canceling the common factor of 2:
(๐ฅ+2)/2
The final simplified form of the rational expression is (๐ฅ+2)/2, with the restriction that ๐ฅ cannot be equal to 3, as that would cause a division by zero in the denominator.