Simplify (x^(1/2+1))/(1/2+1)

$\frac{x^{\frac{1}{2} + 1}}{\frac{1}{2} + 1}$

Simplify the numerator.

Write $1$ as a fraction with a common denominator.

$\frac{x^{\frac{1}{2} + \frac{2}{2}}}{\frac{1}{2} + 1}$

Combine the numerators over the common denominator.

$\frac{x^{\frac{1 + 2}{2}}}{\frac{1}{2} + 1}$

Add $1$ and $2$ .

$\frac{x^{\frac{3}{2}}}{\frac{1}{2} + 1}$

Simplify the denominator.

Write $1$ as a fraction with a common denominator.

$\frac{x^{\frac{3}{2}}}{\frac{1}{2} + \frac{2}{2}}$

Combine the numerators over the common denominator.

$\frac{x^{\frac{3}{2}}}{\frac{1 + 2}{2}}$

Add $1$ and $2$ .

$\frac{x^{\frac{3}{2}}}{\frac{3}{2}}$

Multiply the numerator by the reciprocal of the denominator.

$x^{\frac{3}{2}} \frac{2}{3}$

Combine $x^{\frac{3}{2}}$ and $\frac{2}{3}$ .

$\frac{x^{\frac{3}{2}} \cdot 2}{3}$

Move $2$ to the left of $x^{\frac{3}{2}}$ .

$\frac{2 x^{\frac{3}{2}}}{3}$