Basic Math Examples

$\frac{3 {(a + h)}^{2} + 2 - 6 (a + h) - 3 a^{2} + 6 a - 2}{h}$

Step 1

Simplify the numerator.

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Step 1.1

Subtract $2$ from $2$ .

$\frac{3 {(a + h)}^{2} - 6 (a + h) - 3 a^{2} + 6 a + 0}{h}$

Step 1.2

Add $3 {(a + h)}^{2} - 6 (a + h) - 3 a^{2} + 6 a$ and $0$ .

$\frac{3 {(a + h)}^{2} - 6 (a + h) - 3 a^{2} + 6 a}{h}$

Step 1.3

Factor $3$ out of $3 {(a + h)}^{2} - 6 (a + h) - 3 a^{2} + 6 a$ .

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Step 1.3.1

Factor $3$ out of $3 {(a + h)}^{2}$ .

$\frac{3 ({(a + h)}^{2}) - 6 (a + h) - 3 a^{2} + 6 a}{h}$

Step 1.3.2

Factor $3$ out of $- 6 (a + h)$ .

$\frac{3 ({(a + h)}^{2}) + 3 (- 2 (a + h)) - 3 a^{2} + 6 a}{h}$

Step 1.3.3

Factor $3$ out of $- 3 a^{2}$ .

$\frac{3 ({(a + h)}^{2}) + 3 (- 2 (a + h)) + 3 (- a^{2}) + 6 a}{h}$

Step 1.3.4

Factor $3$ out of $6 a$ .

$\frac{3 ({(a + h)}^{2}) + 3 (- 2 (a + h)) + 3 (- a^{2}) + 3 (2 a)}{h}$

Step 1.3.5

Factor $3$ out of $3 ({(a + h)}^{2}) + 3 (- 2 (a + h))$ .

$\frac{3 ({(a + h)}^{2} - 2 (a + h)) + 3 (- a^{2}) + 3 (2 a)}{h}$

Step 1.3.6

Factor $3$ out of $3 ({(a + h)}^{2} - 2 (a + h)) + 3 (- a^{2})$ .

$\frac{3 ({(a + h)}^{2} - 2 (a + h) - a^{2}) + 3 (2 a)}{h}$

Step 1.3.7

Factor $3$ out of $3 ({(a + h)}^{2} - 2 (a + h) - a^{2}) + 3 (2 a)$ .

$\frac{3 ({(a + h)}^{2} - 2 (a + h) - a^{2} + 2 a)}{h}$

Step 1.4

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

$\frac{3 ((a + h) (a + h) - 2 (a + h) - a^{2} + 2 a)}{h}$

Step 1.5

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

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Step 1.5.1

Apply the distributive property.

$\frac{3 (a (a + h) + h (a + h) - 2 (a + h) - a^{2} + 2 a)}{h}$

Step 1.5.2

Apply the distributive property.

$\frac{3 (a \cdot a + a h + h (a + h) - 2 (a + h) - a^{2} + 2 a)}{h}$

Step 1.5.3

Apply the distributive property.

$\frac{3 (a \cdot a + a h + h a + h \cdot h - 2 (a + h) - a^{2} + 2 a)}{h}$

Step 1.6

Simplify and combine like terms.

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Step 1.6.1

Simplify each term.

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Step 1.6.1.1

Multiply $a$ by $a$ .

$\frac{3 (a^{2} + a h + h a + h \cdot h - 2 (a + h) - a^{2} + 2 a)}{h}$

Step 1.6.1.2

Multiply $h$ by $h$ .

$\frac{3 (a^{2} + a h + h a + h^{2} - 2 (a + h) - a^{2} + 2 a)}{h}$

Step 1.6.2

Add $a h$ and $h a$ .

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Step 1.6.2.1

Reorder $h$ and $a$ .

$\frac{3 (a^{2} + a h + a h + h^{2} - 2 (a + h) - a^{2} + 2 a)}{h}$

Step 1.6.2.2

Add $a h$ and $a h$ .

$\frac{3 (a^{2} + 2 a h + h^{2} - 2 (a + h) - a^{2} + 2 a)}{h}$

Step 1.7

Apply the distributive property.

$\frac{3 (a^{2} + 2 a h + h^{2} - 2 a - 2 h - a^{2} + 2 a)}{h}$

Step 1.8

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

$\frac{3 (2 a h + h^{2} - 2 a - 2 h + 0 + 2 a)}{h}$

Step 1.9

Add $2 a h$ and $0$ .

$\frac{3 (h^{2} - 2 a - 2 h + 2 a h + 2 a)}{h}$

Step 1.10

Add $- 2 a$ and $2 a$ .

$\frac{3 (h^{2} - 2 h + 2 a h + 0)}{h}$

Step 1.11

Add $h^{2} - 2 h + 2 a h$ and $0$ .

$\frac{3 (h^{2} - 2 h + 2 a h)}{h}$

Step 1.12

Factor $h$ out of $h^{2} - 2 h + 2 a h$ .

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Step 1.12.1

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

$\frac{3 (h \cdot h - 2 h + 2 a h)}{h}$

Step 1.12.2

Factor $h$ out of $- 2 h$ .

$\frac{3 (h \cdot h + h \cdot - 2 + 2 a h)}{h}$

Step 1.12.3

Factor $h$ out of $2 a h$ .

$\frac{3 (h \cdot h + h \cdot - 2 + h (2 a))}{h}$

Step 1.12.4

Factor $h$ out of $h \cdot h + h \cdot - 2$ .

$\frac{3 (h (h - 2) + h (2 a))}{h}$

Step 1.12.5

Factor $h$ out of $h (h - 2) + h (2 a)$ .

$\frac{3 (h (h - 2 + 2 a))}{h}$

$\frac{3 h (h - 2 + 2 a)}{h}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $h$ .

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Step 2.1.1

Cancel the common factor.

$\frac{3 h (h - 2 + 2 a)}{h}$

Step 2.1.2

Divide $3 (h - 2 + 2 a)$ by $1$ .

$3 (h - 2 + 2 a)$

Step 2.2

Apply the distributive property.

$3 h + 3 \cdot - 2 + 3 (2 a)$

Step 3

Simplify.

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Step 3.1

Multiply $3$ by $- 2$ .

$3 h - 6 + 3 (2 a)$

Step 3.2

Multiply $2$ by $3$ .

$3 h - 6 + 6 a$

Step 4

Move $- 6$ .

$3 h + 6 a - 6$

Step 5

Reorder $3 h$ and $6 a$ .

$6 a + 3 h - 6$