Calculus Examples

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

Step 1

Simplify terms.

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Multiply $\frac{1}{2 \sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

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

Step 1.1.2

Combine and simplify the denominator.

Tap for more steps...

Step 1.1.2.1

Multiply $\frac{1}{2 \sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

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

Step 1.1.2.2

Move $\sqrt{x}$ .

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

Step 1.1.2.3

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

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

Step 1.1.2.4

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

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

Step 1.1.2.5

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

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

Step 1.1.2.6

Add $1$ and $1$ .

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

Step 1.1.2.7

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

Tap for more steps...

Step 1.1.2.7.1

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

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

Step 1.1.2.7.2

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

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

Step 1.1.2.7.3

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

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

Step 1.1.2.7.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.1.2.7.4.1

Cancel the common factor.

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

Step 1.1.2.7.4.2

Rewrite the expression.

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

Step 1.1.2.7.5

Simplify.

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

Step 1.2

Rewrite ${(\frac{\sqrt{x}}{2} - \frac{\sqrt{x}}{2 x})}^{2}$ as $(\frac{\sqrt{x}}{2} - \frac{\sqrt{x}}{2 x}) (\frac{\sqrt{x}}{2} - \frac{\sqrt{x}}{2 x})$ .

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

Step 2

Expand $(\frac{\sqrt{x}}{2} - \frac{\sqrt{x}}{2 x}) (\frac{\sqrt{x}}{2} - \frac{\sqrt{x}}{2 x})$ using the FOIL Method.

Tap for more steps...

Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Multiply $\frac{\sqrt{x}}{2} \cdot \frac{\sqrt{x}}{2}$ .

Tap for more steps...

Step 3.1.1.1

Multiply $\frac{\sqrt{x}}{2}$ by $\frac{\sqrt{x}}{2}$ .

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

Step 3.1.1.2

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

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

Step 3.1.1.3

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

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

Step 3.1.1.4

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

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

Step 3.1.1.5

Add $1$ and $1$ .

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

Step 3.1.1.6

Multiply $2$ by $2$ .

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

Step 3.1.2

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

Tap for more steps...

Step 3.1.2.1

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

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

Step 3.1.2.2

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

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

Step 3.1.2.3

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

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

Step 3.1.2.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.1.2.4.1

Cancel the common factor.

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

Step 3.1.2.4.2

Rewrite the expression.

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

Step 3.1.2.5

Simplify.

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

Step 3.1.3

Rewrite using the commutative property of multiplication.

$\frac{x}{4} - \frac{\sqrt{x}}{2} \cdot \frac{\sqrt{x}}{2 x} - \frac{\sqrt{x}}{2 x} \cdot \frac{\sqrt{x}}{2} - \frac{\sqrt{x}}{2 x} (- \frac{\sqrt{x}}{2 x})$

Step 3.1.4

Multiply $- \frac{\sqrt{x}}{2} \cdot \frac{\sqrt{x}}{2 x}$ .

Tap for more steps...

Step 3.1.4.1

Multiply $\frac{\sqrt{x}}{2 x}$ by $\frac{\sqrt{x}}{2}$ .

$\frac{x}{4} - \frac{\sqrt{x} \sqrt{x}}{2 x \cdot 2} - \frac{\sqrt{x}}{2 x} \cdot \frac{\sqrt{x}}{2} - \frac{\sqrt{x}}{2 x} (- \frac{\sqrt{x}}{2 x})$

Step 3.1.4.2

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

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

Step 3.1.4.3

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

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

Step 3.1.4.4

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

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

Step 3.1.4.5

Add $1$ and $1$ .

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

Step 3.1.4.6

Multiply $2$ by $2$ .

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

Step 3.1.5

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

Tap for more steps...

Step 3.1.5.1

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

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

Step 3.1.5.2

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

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

Step 3.1.5.3

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

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

Step 3.1.5.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.1.5.4.1

Cancel the common factor.

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

Step 3.1.5.4.2

Rewrite the expression.

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

Step 3.1.5.5

Simplify.

$\frac{x}{4} - \frac{x}{4 x} - \frac{\sqrt{x}}{2 x} \cdot \frac{\sqrt{x}}{2} - \frac{\sqrt{x}}{2 x} (- \frac{\sqrt{x}}{2 x})$

Step 3.1.6

Cancel the common factor of $x$ .

Tap for more steps...

Step 3.1.6.1

Cancel the common factor.

$\frac{x}{4} - \frac{x}{4 x} - \frac{\sqrt{x}}{2 x} \cdot \frac{\sqrt{x}}{2} - \frac{\sqrt{x}}{2 x} (- \frac{\sqrt{x}}{2 x})$

Step 3.1.6.2

Rewrite the expression.

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

Step 3.1.7

Multiply $- \frac{\sqrt{x}}{2 x} \cdot \frac{\sqrt{x}}{2}$ .

Tap for more steps...

Step 3.1.7.1

Multiply $\frac{\sqrt{x}}{2}$ by $\frac{\sqrt{x}}{2 x}$ .

$\frac{x}{4} - \frac{1}{4} - \frac{\sqrt{x} \sqrt{x}}{2 (2 x)} - \frac{\sqrt{x}}{2 x} (- \frac{\sqrt{x}}{2 x})$

Step 3.1.7.2

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

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

Step 3.1.7.3

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

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

Step 3.1.7.4

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

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

Step 3.1.7.5

Add $1$ and $1$ .

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

Step 3.1.7.6

Multiply $2$ by $2$ .

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

Step 3.1.8

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

Tap for more steps...

Step 3.1.8.1

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

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

Step 3.1.8.2

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

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

Step 3.1.8.3

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

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

Step 3.1.8.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.1.8.4.1

Cancel the common factor.

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

Step 3.1.8.4.2

Rewrite the expression.

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

Step 3.1.8.5

Simplify.

$\frac{x}{4} - \frac{1}{4} - \frac{x}{4 x} - \frac{\sqrt{x}}{2 x} (- \frac{\sqrt{x}}{2 x})$

Step 3.1.9

Cancel the common factor of $x$ .

Tap for more steps...

Step 3.1.9.1

Cancel the common factor.

$\frac{x}{4} - \frac{1}{4} - \frac{x}{4 x} - \frac{\sqrt{x}}{2 x} (- \frac{\sqrt{x}}{2 x})$

Step 3.1.9.2

Rewrite the expression.

$\frac{x}{4} - \frac{1}{4} - \frac{1}{4} - \frac{\sqrt{x}}{2 x} (- \frac{\sqrt{x}}{2 x})$

Step 3.1.10

Multiply $- \frac{\sqrt{x}}{2 x} (- \frac{\sqrt{x}}{2 x})$ .

Tap for more steps...

Step 3.1.10.1

Multiply $- 1$ by $- 1$ .

$\frac{x}{4} - \frac{1}{4} - \frac{1}{4} + 1 \frac{\sqrt{x}}{2 x} \frac{\sqrt{x}}{2 x}$

Step 3.1.10.2

Multiply $\frac{\sqrt{x}}{2 x}$ by $1$ .

$\frac{x}{4} - \frac{1}{4} - \frac{1}{4} + \frac{\sqrt{x}}{2 x} \cdot \frac{\sqrt{x}}{2 x}$

Step 3.1.10.3

Multiply $\frac{\sqrt{x}}{2 x}$ by $\frac{\sqrt{x}}{2 x}$ .

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

Step 3.1.10.4

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

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

Step 3.1.10.5

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

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

Step 3.1.10.6

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

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

Step 3.1.10.7

Add $1$ and $1$ .

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

Step 3.1.10.8

Multiply $2$ by $2$ .

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

Step 3.1.10.9

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

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

Step 3.1.10.10

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

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

Step 3.1.10.11

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

$\frac{x}{4} - \frac{1}{4} - \frac{1}{4} + \frac{{\sqrt{x}}^{2}}{4 x^{1 + 1}}$

Step 3.1.10.12

Add $1$ and $1$ .

$\frac{x}{4} - \frac{1}{4} - \frac{1}{4} + \frac{{\sqrt{x}}^{2}}{4 x^{2}}$

Step 3.1.11

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

Tap for more steps...

Step 3.1.11.1

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

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

Step 3.1.11.2

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

$\frac{x}{4} - \frac{1}{4} - \frac{1}{4} + \frac{x^{\frac{1}{2} \cdot 2}}{4 x^{2}}$

Step 3.1.11.3

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

$\frac{x}{4} - \frac{1}{4} - \frac{1}{4} + \frac{x^{\frac{2}{2}}}{4 x^{2}}$

Step 3.1.11.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.1.11.4.1

Cancel the common factor.

$\frac{x}{4} - \frac{1}{4} - \frac{1}{4} + \frac{x^{\frac{2}{2}}}{4 x^{2}}$

Step 3.1.11.4.2

Rewrite the expression.

$\frac{x}{4} - \frac{1}{4} - \frac{1}{4} + \frac{x^{1}}{4 x^{2}}$

Step 3.1.11.5

Simplify.

$\frac{x}{4} - \frac{1}{4} - \frac{1}{4} + \frac{x}{4 x^{2}}$

Step 3.1.12

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

Tap for more steps...

Step 3.1.12.1

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

$\frac{x}{4} - \frac{1}{4} - \frac{1}{4} + \frac{x^{1}}{4 x^{2}}$

Step 3.1.12.2

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

$\frac{x}{4} - \frac{1}{4} - \frac{1}{4} + \frac{x \cdot 1}{4 x^{2}}$

Step 3.1.12.3

Cancel the common factors.

Tap for more steps...

Step 3.1.12.3.1

Factor $x$ out of $4 x^{2}$ .

$\frac{x}{4} - \frac{1}{4} - \frac{1}{4} + \frac{x \cdot 1}{x (4 x)}$

Step 3.1.12.3.2

Cancel the common factor.

$\frac{x}{4} - \frac{1}{4} - \frac{1}{4} + \frac{x \cdot 1}{x (4 x)}$

Step 3.1.12.3.3

Rewrite the expression.

$\frac{x}{4} - \frac{1}{4} - \frac{1}{4} + \frac{1}{4 x}$

Step 3.2

Subtract $\frac{1}{4}$ from $- \frac{1}{4}$ .

$\frac{x}{4} - 2 (\frac{1}{4}) + \frac{1}{4 x}$

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.1.1

Factor $2$ out of $- 2$ .

$\frac{x}{4} + 2 (- 1) \frac{1}{4} + \frac{1}{4 x}$

Step 4.1.2

Factor $2$ out of $4$ .

$\frac{x}{4} + 2 \cdot - 1 \frac{1}{2 \cdot 2} + \frac{1}{4 x}$

Step 4.1.3

Cancel the common factor.

$\frac{x}{4} + 2 \cdot - 1 \frac{1}{2 \cdot 2} + \frac{1}{4 x}$

Step 4.1.4

Rewrite the expression.

$\frac{x}{4} - 1 (\frac{1}{2}) + \frac{1}{4 x}$

Step 4.2

Rewrite $- 1 (\frac{1}{2})$ as $- (\frac{1}{2})$ .

$\frac{x}{4} - \frac{1}{2} + \frac{1}{4 x}$