Answer
What Hung did wrong was that he did not multiply both the numerator and the denominator by the denominator. This would have kept the rational expression equivalent to the original rational expression.
$4\sqrt {14}$
Work Step by Step
What Hung did wrong was that he did not multiply both the numerator and the denominator by the denominator. This would have kept the rational expression equivalent to the original rational expression.
To simplify the expression, we can't leave radicals in the denominator, so to get rid of radicals in the denominator, we multiply both numerator and denominator by the denominator:
$\frac{8\sqrt {7x}}{\sqrt {2x}} • \frac{\sqrt {2x}}{\sqrt {2x}}$
Multiply to simplify:
$\frac{8\sqrt {14x^2}}{\sqrt {4x^2}}$
Take the square roots:
$\frac{8 • x\sqrt {14}}{2x}$
Multiply coefficients:
$\frac{8x\sqrt {14}}{2x}$
Cancel out factors that are common to both the numerator and denominator:
$4\sqrt {14}$
