Answer
$\frac{3 \sqrt {3x}}{7x}$
Work Step by Step
Multiply both the numerator and denominator by a factor that will eliminate the radical in the denominator. That factor, in this exercise, will be $\sqrt {2x}$:
$\frac{3 \sqrt {6}}{7 \sqrt {2x}} \bullet \frac{\sqrt {2x}}{\sqrt {2x}}$
Multiply to simplify:
$\frac{3 \sqrt {12x}}{7 \sqrt {4x^2}}$
Take the square roots of all perfect squares:
$\frac{3 \sqrt {12x}}{14x}$
Rewrite the radicand in the numerator as the product of a perfect square and other factors:
$\frac{3 \sqrt {(4 \bullet 3)(x)}}{14x}$
Take the square root of the perfect square in the radicand of the numerator:
$\frac{6 \sqrt {3x}}{14x}$
Cancel out common factors in the numerator and denominator:
$\frac{3 \sqrt {3x}}{7x}$
