Finite Math Examples

$\frac{{(x + h)}^{2} - 6 - x^{2} - 6}{h}$

Step 1

Rewrite ${(x + h)}^{2}$ as $(x + h) (x + h)$ .

$\frac{(x + h) (x + h) - 6 - x^{2} - 6}{h}$

Step 2

Expand $(x + h) (x + h)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$\frac{x (x + h) + h (x + h) - 6 - x^{2} - 6}{h}$

Step 2.2

Apply the distributive property.

$\frac{x \cdot x + x h + h (x + h) - 6 - x^{2} - 6}{h}$

Step 2.3

Apply the distributive property.

$\frac{x \cdot x + x h + h x + h \cdot h - 6 - x^{2} - 6}{h}$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $x$ by $x$ .

$\frac{x^{2} + x h + h x + h \cdot h - 6 - x^{2} - 6}{h}$

Step 3.1.2

Multiply $h$ by $h$ .

$\frac{x^{2} + x h + h x + h^{2} - 6 - x^{2} - 6}{h}$

Step 3.2

Add $x h$ and $h x$ .

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Step 3.2.1

Reorder $x$ and $h$ .

$\frac{x^{2} + h x + h x + h^{2} - 6 - x^{2} - 6}{h}$

Step 3.2.2

Add $h x$ and $h x$ .

$\frac{x^{2} + 2 h x + h^{2} - 6 - x^{2} - 6}{h}$

Step 4

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

$\frac{2 h x + h^{2} - 6 + 0 - 6}{h}$

Step 5

Add $2 h x$ and $0$ .

$\frac{2 h x + h^{2} - 6 - 6}{h}$

Step 6

Subtract $6$ from $- 6$ .

$\frac{2 h x + h^{2} - 12}{h}$