Algebra Examples

$\sqrt{21 (x - 1)} \div \sqrt{7 x^{2}}$

Step 1

Rewrite the division as a fraction.

$\frac{\sqrt{21 (x - 1)}}{\sqrt{7 x^{2}}}$

Step 2

Combine $\sqrt{21 (x - 1)}$ and $\sqrt{7 x^{2}}$ into a single radical.

$\sqrt{\frac{21 (x - 1)}{7 x^{2}}}$

Step 3

Reduce the expression $\frac{21 (x - 1)}{7 x^{2}}$ by cancelling the common factors.

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Step 3.1

Factor $7$ out of $21 (x - 1)$ .

$\sqrt{\frac{7 (3 (x - 1))}{7 x^{2}}}$

Step 3.2

Factor $7$ out of $7 x^{2}$ .

$\sqrt{\frac{7 (3 (x - 1))}{7 (x^{2})}}$

Step 3.3

Cancel the common factor.

$\sqrt{\frac{7 (3 (x - 1))}{7 x^{2}}}$

Step 3.4

Rewrite the expression.

$\sqrt{\frac{3 (x - 1)}{x^{2}}}$

Step 4

Rewrite $\frac{3 (x - 1)}{x^{2}}$ as ${(\frac{1}{x})}^{2} (3 (x - 1))$ .

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Step 4.1

Factor the perfect power $1^{2}$ out of $3 (x - 1)$ .

$\sqrt{\frac{1^{2} (3 (x - 1))}{x^{2}}}$

Step 4.2

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

$\sqrt{\frac{1^{2} (3 (x - 1))}{x^{2} \cdot 1}}$

Step 4.3

Rearrange the fraction $\frac{1^{2} (3 (x - 1))}{x^{2} \cdot 1}$ .

$\sqrt{{(\frac{1}{x})}^{2} (3 (x - 1))}$

Step 5

Pull terms out from under the radical.

$\frac{1}{x} \sqrt{3 (x - 1)}$

Step 6

Combine $\frac{1}{x}$ and $\sqrt{3 (x - 1)}$ .

$\frac{\sqrt{3 (x - 1)}}{x}$