Simplify x^(3/2)( square root of x-1/( square root of x))

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

Step 1

Simplify each term.

Multiply $\frac{1}{\sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

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

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

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

Raise $\sqrt{x}$ to the power of $1$ .

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

Raise $\sqrt{x}$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $1$ .

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

Rewrite ${\sqrt{x}}^{2}$ as $x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

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

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Step 2

Apply the distributive property.

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

Step 3

Multiply $x^{\frac{3}{2}} \sqrt{x}$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Combine the numerators over the common denominator.

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

Add $3$ and $1$ .

$x^{\frac{4}{2}} + x^{\frac{3}{2}} (- \frac{\sqrt{x}}{x})$

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $2$ by $1$ .

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

Step 4

Rewrite using the commutative property of multiplication.

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

Step 5

Simplify each term.

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

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

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Combine the numerators over the common denominator.

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

Add $1$ and $3$ .

$x^{2} - \frac{x^{\frac{4}{2}}}{x}$

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

$x^{2} - \frac{x^{\frac{2 \cdot 2}{2 \cdot 1}}}{x}$

Rewrite the expression.

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

Divide $2$ by $1$ .

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

Cancel the common factor of $x^{2}$ and $x$ .

Factor $x$ out of $x^{2}$ .

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

Cancel the common factors.

Raise $x$ to the power of $1$ .

$x^{2} - \frac{x \cdot x}{x^{1}}$

Factor $x$ out of $x^{1}$ .

$x^{2} - \frac{x \cdot x}{x \cdot 1}$

Cancel the common factor.

$x^{2} - \frac{x \cdot x}{x \cdot 1}$

Rewrite the expression.

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

Divide $x$ by $1$ .

$x^{2} - x$

Simplify x^(3/2)( square root of x-1/( square root of x))

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