Simplify ( square root of 30(x-1))÷( square root of 5x^2)

$\sqrt{30 (x - 1)} \div \sqrt{5 x^{2}}$

Step 1

Rewrite the division as a fraction.

$\frac{\sqrt{30 (x - 1)}}{\sqrt{5 x^{2}}}$

Step 2

Combine $\sqrt{30 (x - 1)}$ and $\sqrt{5 x^{2}}$ into a single radical.

$\sqrt{\frac{30 (x - 1)}{5 x^{2}}}$

Step 3

Reduce the expression $\frac{30 (x - 1)}{5 x^{2}}$ by cancelling the common factors.

Factor $5$ out of $30 (x - 1)$ .

$\sqrt{\frac{5 (6 (x - 1))}{5 x^{2}}}$

Factor $5$ out of $5 x^{2}$ .

$\sqrt{\frac{5 (6 (x - 1))}{5 (x^{2})}}$

Cancel the common factor.

$\sqrt{\frac{5 (6 (x - 1))}{5 x^{2}}}$

Rewrite the expression.

$\sqrt{\frac{6 (x - 1)}{x^{2}}}$

Step 4

Rewrite $\frac{6 (x - 1)}{x^{2}}$ as ${(\frac{1}{x})}^{2} (6 (x - 1))$ .

Factor the perfect power $1^{2}$ out of $6 (x - 1)$ .

$\sqrt{\frac{1^{2} (6 (x - 1))}{x^{2}}}$

Factor the perfect power $x^{2}$ out of $x^{2}$ .

$\sqrt{\frac{1^{2} (6 (x - 1))}{x^{2} \cdot 1}}$

Rearrange the fraction $\frac{1^{2} (6 (x - 1))}{x^{2} \cdot 1}$ .

$\sqrt{{(\frac{1}{x})}^{2} (6 (x - 1))}$

Step 5

Pull terms out from under the radical.

$\frac{1}{x} \sqrt{6 (x - 1)}$

Step 6

Combine $\frac{1}{x}$ and $\sqrt{6 (x - 1)}$ .

$\frac{\sqrt{6 (x - 1)}}{x}$