Precalculus Examples

${(x + 3)}^{\frac{1}{5}} - {(x + 3)}^{\frac{6}{5}}$

Step 1

Factor ${(x + 3)}^{\frac{1}{5}}$ out of ${(x + 3)}^{\frac{1}{5}} - {(x + 3)}^{\frac{6}{5}}$ .

Tap for more steps...

Step 1.1

Multiply by $1$ .

${(x + 3)}^{\frac{1}{5}} \cdot 1 - {(x + 3)}^{\frac{6}{5}}$

Step 1.2

Factor ${(x + 3)}^{\frac{1}{5}}$ out of $- {(x + 3)}^{\frac{6}{5}}$ .

${(x + 3)}^{\frac{1}{5}} \cdot 1 + {(x + 3)}^{\frac{1}{5}} (- {(x + 3)}^{\frac{5}{5}})$

Step 1.3

Factor ${(x + 3)}^{\frac{1}{5}}$ out of ${(x + 3)}^{\frac{1}{5}} \cdot 1 + {(x + 3)}^{\frac{1}{5}} (- {(x + 3)}^{\frac{5}{5}})$ .

${(x + 3)}^{\frac{1}{5}} (1 - {(x + 3)}^{\frac{5}{5}})$

Step 2

Divide $5$ by $5$ .

${(x + 3)}^{\frac{1}{5}} (1 - {(x + 3)}^{1})$

Step 3

Simplify.

${(x + 3)}^{\frac{1}{5}} (1 - (x + 3))$

Step 4

Apply the distributive property.

${(x + 3)}^{\frac{1}{5}} (1 - x - 1 \cdot 3)$

Step 5

Multiply $- 1$ by $3$ .

${(x + 3)}^{\frac{1}{5}} (1 - x - 3)$

Step 6

Subtract $3$ from $1$ .

${(x + 3)}^{\frac{1}{5}} (- x - 2)$

Step 7

Factor.

Tap for more steps...

Step 7.1

Factor $- 1$ out of $- x - 2$ .

Tap for more steps...

Step 7.1.1

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

${(x + 3)}^{\frac{1}{5}} (- (x) - 2)$

Step 7.1.2

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

${(x + 3)}^{\frac{1}{5}} (- (x) - 1 (2))$

Step 7.1.3

Factor $- 1$ out of $- (x) - 1 (2)$ .

${(x + 3)}^{\frac{1}{5}} (- (x + 2))$

Step 7.2

Remove unnecessary parentheses.

${(x + 3)}^{\frac{1}{5}} \cdot - 1 (x + 2)$

Step 8

Factor out negative.

$- ({(x + 3)}^{\frac{1}{5}} (x + 2))$

Step 9

Remove unnecessary parentheses.

$- {(x + 3)}^{\frac{1}{5}} (x + 2)$