Simplify (6x^5-9x)/((8x^4-12)/8)

$\frac{6 x^{5} - 9 x}{\frac{8 x^{4} - 12}{8}}$

Cancel the common factor of $8 x^{4} - 12$ and $8$ .

Factor $4$ out of $8 x^{4}$ .

$\frac{6 x^{5} - 9 x}{\frac{4 (2 x^{4}) - 12}{8}}$

Factor $4$ out of $- 12$ .

$\frac{6 x^{5} - 9 x}{\frac{4 (2 x^{4}) + 4 (- 3)}{8}}$

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

$\frac{6 x^{5} - 9 x}{\frac{4 (2 x^{4} - 3)}{8}}$

Cancel the common factors.

Factor $4$ out of $8$ .

$\frac{6 x^{5} - 9 x}{\frac{4 (2 x^{4} - 3)}{4 (2)}}$

Cancel the common factor.

$\frac{6 x^{5} - 9 x}{\frac{4 (2 x^{4} - 3)}{4 \cdot 2}}$

Rewrite the expression.

$\frac{6 x^{5} - 9 x}{\frac{2 x^{4} - 3}{2}}$

Multiply the numerator by the reciprocal of the denominator.

$(6 x^{5} - 9 x) \frac{2}{2 x^{4} - 3}$

Multiply $6 x^{5} - 9 x$ by $\frac{2}{2 x^{4} - 3}$ .

$\frac{(6 x^{5} - 9 x) \cdot 2}{2 x^{4} - 3}$

Simplify the numerator.

Factor $3 x$ out of $6 x^{5} - 9 x$ .

Factor $3 x$ out of $6 x^{5}$ .

$\frac{(3 x (2 x^{4}) - 9 x) \cdot 2}{2 x^{4} - 3}$

Factor $3 x$ out of $- 9 x$ .

$\frac{(3 x (2 x^{4}) + 3 x (- 3)) \cdot 2}{2 x^{4} - 3}$

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

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

Multiply $2$ by $3$ .

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

Cancel the common factor of $2 x^{4} - 3$ .

Cancel the common factor.

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

Divide $6 x$ by $1$ .

$6 x$