Calculus Examples

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

Step 1

Remove parentheses.

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

Step 2

Simplify the numerator.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Multiply $2$ by $- 1$ .

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

Step 2.4

Subtract $x^{2}$ from $x^{2}$ .

$\frac{h^{2} + 2 x h + 2 h + 2 x + 0 - 2 x}{h}$

Step 2.5

Add $h^{2}$ and $0$ .

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

Step 2.6

Subtract $2 x$ from $2 x$ .

$\frac{h^{2} + 2 x h + 2 h + 0}{h}$

Step 2.7

Add $h^{2} + 2 x h + 2 h$ and $0$ .

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

Step 2.8

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

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Step 2.8.1

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

$\frac{h \cdot h + 2 x h + 2 h}{h}$

Step 2.8.2

Factor $h$ out of $2 x h$ .

$\frac{h \cdot h + h (2 x) + 2 h}{h}$

Step 2.8.3

Factor $h$ out of $2 h$ .

$\frac{h \cdot h + h (2 x) + h \cdot 2}{h}$

Step 2.8.4

Factor $h$ out of $h \cdot h + h (2 x)$ .

$\frac{h (h + 2 x) + h \cdot 2}{h}$

Step 2.8.5

Factor $h$ out of $h (h + 2 x) + h \cdot 2$ .

$\frac{h (h + 2 x + 2)}{h}$

Step 3

Cancel the common factor of $h$ .

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Step 3.1

Cancel the common factor.

$\frac{h (h + 2 x + 2)}{h}$

Step 3.2

Divide $h + 2 x + 2$ by $1$ .

$h + 2 x + 2$