To simplify the expression \(\frac{\sqrt{315x^6}}{\sqrt{5x}}\), we can first use the property of square roots that states \(\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}\).
Applying this property, we have:
\[ \frac{\sqrt{315x^6}}{\sqrt{5x}} = \sqrt{\frac{315x^6}{5x}} \]
Now, we can simplify the fraction inside the square root:
\[ \frac{315x^6}{5x} = \frac{315}{5} \cdot \frac{x^6}{x} \]
Calculating \(\frac{315}{5}\):
\[ \frac{315}{5} = 63 \]
And simplifying \(\frac{x^6}{x}\):
\[ \frac{x^6}{x} = x^{6-1} = x^5 \]
Thus, we have:
\[ \sqrt{\frac{315x^6}{5x}} = \sqrt{63x^5} \]
Next, we can separate this into its components:
\[ \sqrt{63x^5} = \sqrt{63} \cdot \sqrt{x^5} \]
The square root of \(x^5\) can be simplified further:
\[ \sqrt{x^5} = \sqrt{x^4 \cdot x} = \sqrt{x^4} \cdot \sqrt{x} = x^2 \cdot \sqrt{x} \]
So we have:
\[ \sqrt{63x^5} = \sqrt{63} \cdot x^2 \cdot \sqrt{x} \]
Finally, we can express \(\sqrt{63}\) in a simpler radical form. \(63 = 9 \cdot 7\), and we know that \(\sqrt{9} = 3\):
\[ \sqrt{63} = \sqrt{9 \cdot 7} = \sqrt{9} \cdot \sqrt{7} = 3\sqrt{7} \]
Combining all the parts, we get:
\[ \sqrt{63x^5} = 3\sqrt{7} \cdot x^2 \cdot \sqrt{x} = 3x^2\sqrt{7x} \]
Thus, the simplified expression is:
\[ \frac{\sqrt{315x^6}}{\sqrt{5x}} = 3x^2 \sqrt{7x} \]
So the final answer is:
\[ \boxed{3x^2 \sqrt{7x}} \]