Simplify 1/(2x^3-4)-3/(3x^3-6)

$\frac{1}{2 x^{3} - 4} - \frac{3}{3 x^{3} - 6}$

Simplify each term.

Factor $2$ out of $2 x^{3} - 4$ .

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

$\frac{1}{2 (x^{3}) - 4} - \frac{3}{3 x^{3} - 6}$

Factor $2$ out of $- 4$ .

$\frac{1}{2 x^{3} + 2 \cdot - 2} - \frac{3}{3 x^{3} - 6}$

Factor $2$ out of $2 x^{3} + 2 \cdot - 2$ .

$\frac{1}{2 (x^{3} - 2)} - \frac{3}{3 x^{3} - 6}$

Cancel the common factor of $3$ and $3 x^{3} - 6$ .

Factor $3$ out of $3$ .

$\frac{1}{2 (x^{3} - 2)} - \frac{3 \cdot 1}{3 x^{3} - 6}$

Cancel the common factors.

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

$\frac{1}{2 (x^{3} - 2)} - \frac{3 \cdot 1}{3 (x^{3}) - 6}$

Factor $3$ out of $- 6$ .

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

Factor $3$ out of $3 (x^{3}) + 3 (- 2)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

To write $- \frac{1}{x^{3} - 2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Write each expression with a common denominator of $2 (x^{3} - 2)$ , by multiplying each by an appropriate factor of $1$ .

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

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

Reorder the factors of $(x^{3} - 2) \cdot 2$ .

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

Combine the numerators over the common denominator.

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

Simplify the expression.

Subtract $2$ from $1$ .

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

Move the negative in front of the fraction.

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