Algebra Examples

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

Step 1

Regroup terms.

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

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

Step 6

Add $- 4$ and $6$ .

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

Step 7

Combine the numerators over the common denominator.

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

Step 8

Add $36$ and $4$ .

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

Step 9

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

Tap for more steps...

Step 9.1

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

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

Step 9.2

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

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

Step 9.3

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

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

Step 9.4

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

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

Step 9.5

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

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