Factor (x+1)^(1/2)-1/3(x+1)^(3/2)

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

Factor ${(x + 1)}^{\frac{1}{2}}$ out of ${(x + 1)}^{\frac{1}{2}} - \frac{1}{3} \cdot {(x + 1)}^{\frac{3}{2}}$ .

Multiply by $1$ .

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

Factor ${(x + 1)}^{\frac{1}{2}}$ out of $- \frac{1}{3} \cdot {(x + 1)}^{\frac{3}{2}}$ .

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

Factor ${(x + 1)}^{\frac{1}{2}}$ out of ${(x + 1)}^{\frac{1}{2}} \cdot 1 + {(x + 1)}^{\frac{1}{2}} (- \frac{1}{3} \cdot {(x + 1)}^{\frac{2}{2}})$ .

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

Factor.

Factor $\frac{1}{3}$ out of each term.

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

Remove unnecessary parentheses.

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

Combine ${(x + 1)}^{\frac{1}{2}}$ and $\frac{1}{3}$ .

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

Divide $2$ by $2$ .

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

Simplify.

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

Apply the distributive property.

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

Rewrite $- 1 x$ as $- x$ .

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

Multiply $- 1$ by $1$ .

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

Subtract $1$ from $3$ .

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

Factor.

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

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

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

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

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

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

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

Remove unnecessary parentheses.

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

Factor out negative.

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

Remove unnecessary parentheses.

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