Simplify the rational expression by rationalizing the denominator.
√12 / √8x
To simplify this expression, we need to rationalize the denominator by multiplying both numerator and denominator by √2.
√12 / √8x
= (√12/√8x) * (√2/√2)
= (√(4*3)/√(4*2* x)) * (√2/√2)
= (2√3/2√(2x)) *1
= √3/√(2x)
Therefore, the simplified expression is √3/√(2x).
To rationalize the denominator, we want to get rid of any square roots in the denominator.
Let's start by simplifying the square roots in both the numerator and the denominator separately.
For the numerator, √12, we can simplify it as:
√12 = √(4 * 3) = √4 * √3 = 2√3
Now, for the denominator, √8x, we can simplify it as:
√8x = √(4 * 2x) = √4 * √(2x) = 2√(2x)
Putting it all together, the rational expression becomes:
2√3 / 2√(2x)
Notice that we have a common factor of 2 in both the numerator and the denominator. We can cancel that out, simplifying the expression further:
(2/2) * (√3 / √(2x)) = 1 * (√3 / √(2x))
Therefore, the simplified expression is:
√3 / √(2x) or (√3) / (√(2x))