Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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

Step 1.2

Combine the numerators over the common denominator.

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

Step 1.3

Add $1$ and $2$ .

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

Step 2

Simplify the denominator.

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Step 2.1

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

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 2.3

Add $1$ and $2$ .

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

Step 3

Multiply the numerator by the reciprocal of the denominator.

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

Step 4

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

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

Step 5

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

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