Divide (x^2-x+5)/( square root of x)

$\frac{x^{2} - x + 5}{\sqrt{x}}$

Step 1

Multiply $\frac{x^{2} - x + 5}{\sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

$\frac{x^{2} - x + 5}{\sqrt{x}} \cdot \frac{\sqrt{x}}{\sqrt{x}}$

Step 2

Combine and simplify the denominator.

Multiply $\frac{x^{2} - x + 5}{\sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Step 3

Reorder factors in $\frac{(x^{2} - x + 5) \sqrt{x}}{x}$ .

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

Step 4

Apply the distributive property.

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

Step 5

Simplify.

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

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

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

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

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

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $2$ .

$\frac{x^{\frac{1 + 4}{2}} + \sqrt{x} (- x) + \sqrt{x} \cdot 5}{x}$

Add $1$ and $4$ .

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

Rewrite using the commutative property of multiplication.

$\frac{x^{\frac{5}{2}} - \sqrt{x} x + \sqrt{x} \cdot 5}{x}$

Move $5$ to the left of $\sqrt{x}$ .

$\frac{x^{\frac{5}{2}} - \sqrt{x} x + 5 \cdot \sqrt{x}}{x}$

$\frac{x^{\frac{5}{2}} - \sqrt{x} x + 5 \sqrt{x}}{x}$

Step 6

Split the fraction $\frac{x^{\frac{5}{2}} - \sqrt{x} x + 5 \sqrt{x}}{x}$ into two fractions.

$\frac{x^{\frac{5}{2}} - \sqrt{x} x}{x} + \frac{5 \sqrt{x}}{x}$

Step 7

Split the fraction $\frac{x^{\frac{5}{2}} - \sqrt{x} x}{x}$ into two fractions.

$\frac{x^{\frac{5}{2}}}{x} + \frac{- \sqrt{x} x}{x} + \frac{5 \sqrt{x}}{x}$

Step 8

Move $x^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$x^{\frac{5}{2}} x^{- 1} + \frac{- \sqrt{x} x}{x} + \frac{5 \sqrt{x}}{x}$

Step 9

Multiply $x^{\frac{5}{2}}$ by $x^{- 1}$ by adding the exponents.

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

$x^{\frac{5}{2} - 1} + \frac{- \sqrt{x} x}{x} + \frac{5 \sqrt{x}}{x}$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x^{\frac{5}{2} - 1 \cdot \frac{2}{2}} + \frac{- \sqrt{x} x}{x} + \frac{5 \sqrt{x}}{x}$

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

$x^{\frac{5}{2} + \frac{- 1 \cdot 2}{2}} + \frac{- \sqrt{x} x}{x} + \frac{5 \sqrt{x}}{x}$

Combine the numerators over the common denominator.

$x^{\frac{5 - 1 \cdot 2}{2}} + \frac{- \sqrt{x} x}{x} + \frac{5 \sqrt{x}}{x}$

Simplify the numerator.

Multiply $- 1$ by $2$ .

$x^{\frac{5 - 2}{2}} + \frac{- \sqrt{x} x}{x} + \frac{5 \sqrt{x}}{x}$

Subtract $2$ from $5$ .

$x^{\frac{3}{2}} + \frac{- \sqrt{x} x}{x} + \frac{5 \sqrt{x}}{x}$

Step 10

Cancel the common factor of $x$ .

Cancel the common factor.

$x^{\frac{3}{2}} + \frac{- \sqrt{x} x}{x} + \frac{5 \sqrt{x}}{x}$

Divide $- \sqrt{x}$ by $1$ .

$x^{\frac{3}{2}} - \sqrt{x} + \frac{5 \sqrt{x}}{x}$

Divide (x^2-x+5)/( square root of x)

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