Factor (6/x)^2-4+(2/x)^2-5x+6

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

Regroup terms.

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

Apply the product rule to $\frac{6}{x}$ .

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

Raise $6$ to the power of $2$ .

$\frac{36}{x^{2}} - 5 x - 4 + {(\frac{2}{x})}^{2} + 6$

Apply the product rule to $\frac{2}{x}$ .

$\frac{36}{x^{2}} - 5 x - 4 + \frac{2^{2}}{x^{2}} + 6$

Raise $2$ to the power of $2$ .

$\frac{36}{x^{2}} - 5 x - 4 + \frac{4}{x^{2}} + 6$

Add $- 4$ and $6$ .

$\frac{36}{x^{2}} - 5 x + \frac{4}{x^{2}} + 2$

Combine the numerators over the common denominator.

$- 5 x + \frac{36 + 4}{x^{2}} + 2$

Add $36$ and $4$ .

$- 5 x + \frac{40}{x^{2}} + 2$

Factor $- 1$ out of $- 5 x + \frac{40}{x^{2}} + 2$ .

Factor $- 1$ out of $- 5 x$ .

$- (5 x) + \frac{40}{x^{2}} + 2$

Factor $- 1$ out of $\frac{40}{x^{2}}$ .

$- (5 x) - \frac{- 40}{x^{2}} + 2$

Rewrite $2$ as $- 1 (- 2)$ .

$- (5 x) - \frac{- 40}{x^{2}} - 1 \cdot - 2$

Factor $- 1$ out of $- (5 x) - \frac{- 40}{x^{2}}$ .

$- (5 x + \frac{- 40}{x^{2}}) - 1 \cdot - 2$

Factor $- 1$ out of $- (5 x + \frac{- 40}{x^{2}}) - 1 \cdot - 2$ .

$- (5 x + \frac{- 40}{x^{2}} - 2)$