Simplify (6/(10x^2))÷(6/(10x^3-60x^2))

$\frac{6}{10 x^{2}} \div \frac{6}{10 x^{3} - 60 x^{2}}$

To divide by a fraction, multiply by its reciprocal.

$\frac{6}{10 x^{2}} \cdot \frac{10 x^{3} - 60 x^{2}}{6}$

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6}{10 x^{2}} \cdot \frac{10 x^{3} - 60 x^{2}}{6}$

Rewrite the expression.

$\frac{1}{10 x^{2}} (10 x^{3} - 60 x^{2})$

Multiply $\frac{1}{10 x^{2}}$ by $10 x^{3} - 60 x^{2}$ .

$\frac{10 x^{3} - 60 x^{2}}{10 x^{2}}$

Factor $10 x^{2}$ out of $10 x^{3} - 60 x^{2}$ .

Factor $10 x^{2}$ out of $10 x^{3}$ .

$\frac{10 x^{2} (x) - 60 x^{2}}{10 x^{2}}$

Factor $10 x^{2}$ out of $- 60 x^{2}$ .

$\frac{10 x^{2} (x) + 10 x^{2} (- 6)}{10 x^{2}}$

Factor $10 x^{2}$ out of $10 x^{2} (x) + 10 x^{2} (- 6)$ .

$\frac{10 x^{2} (x - 6)}{10 x^{2}}$

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 x^{2} (x - 6)}{10 x^{2}}$

Rewrite the expression.

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

Cancel the common factor of $x^{2}$ .

Cancel the common factor.

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

Divide $x - 6$ by $1$ .

$x - 6$