Calculus Examples

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

Step 1

Multiply the numerator and denominator of the fraction by $4 x$ .

Tap for more steps...

Step 1.1

Multiply $\frac{\frac{1}{4} + \frac{1}{x}}{4 + x}$ by $\frac{4 x}{4 x}$ .

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

Step 1.2

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

Tap for more steps...

Step 3.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 3.1.1

Factor $4$ out of $4 x$ .

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

Step 3.1.2

Cancel the common factor.

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

Step 3.1.3

Rewrite the expression.

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

Step 3.2

Cancel the common factor of $x$ .

Tap for more steps...

Step 3.2.1

Factor $x$ out of $4 x$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

$\frac{x + 4}{4 x \cdot 4 + 4 x \cdot x}$

Step 4

Simplify the denominator.

Tap for more steps...

Step 4.1

Multiply $4$ by $4$ .

$\frac{x + 4}{16 x + 4 x \cdot x}$

Step 4.2

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 4.2.1

Move $x$ .

$\frac{x + 4}{16 x + 4 (x \cdot x)}$

Step 4.2.2

Multiply $x$ by $x$ .

$\frac{x + 4}{16 x + 4 x^{2}}$

Step 4.3

Factor $4 x$ out of $16 x + 4 x^{2}$ .

Tap for more steps...

Step 4.3.1

Factor $4 x$ out of $16 x$ .

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

Step 4.3.2

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

$\frac{x + 4}{4 x (4) + 4 x (x)}$

Step 4.3.3

Factor $4 x$ out of $4 x (4) + 4 x (x)$ .

$\frac{x + 4}{4 x (4 + x)}$

Step 5

Cancel the common factor of $x + 4$ and $4 + x$ .

Tap for more steps...

Step 5.1

Reorder terms.

$\frac{x + 4}{4 x (x + 4)}$

Step 5.2

Cancel the common factor.

$\frac{x + 4}{4 x (x + 4)}$

Step 5.3

Rewrite the expression.

$\frac{1}{4 x}$