Basic Math Examples

$\frac{(- 5 - 7 {(3 + h)}^{2}) - (3 + h)}{h}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite ${(3 + h)}^{2}$ as $(3 + h) (3 + h)$ .

$\frac{- 5 - 7 ((3 + h) (3 + h)) - (3 + h)}{h}$

Step 1.2

Expand $(3 + h) (3 + h)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$\frac{- 5 - 7 (3 (3 + h) + h (3 + h)) - (3 + h)}{h}$

Step 1.2.2

Apply the distributive property.

$\frac{- 5 - 7 (3 \cdot 3 + 3 h + h (3 + h)) - (3 + h)}{h}$

Step 1.2.3

Apply the distributive property.

$\frac{- 5 - 7 (3 \cdot 3 + 3 h + h \cdot 3 + h \cdot h) - (3 + h)}{h}$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $3$ by $3$ .

$\frac{- 5 - 7 (9 + 3 h + h \cdot 3 + h \cdot h) - (3 + h)}{h}$

Step 1.3.1.2

Move $3$ to the left of $h$ .

$\frac{- 5 - 7 (9 + 3 h + 3 \cdot h + h \cdot h) - (3 + h)}{h}$

Step 1.3.1.3

Multiply $h$ by $h$ .

$\frac{- 5 - 7 (9 + 3 h + 3 h + h^{2}) - (3 + h)}{h}$

Step 1.3.2

Add $3 h$ and $3 h$ .

$\frac{- 5 - 7 (9 + 6 h + h^{2}) - (3 + h)}{h}$

Step 1.4

Apply the distributive property.

$\frac{- 5 - 7 \cdot 9 - 7 (6 h) - 7 h^{2} - (3 + h)}{h}$

Step 1.5

Simplify.

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Step 1.5.1

Multiply $- 7$ by $9$ .

$\frac{- 5 - 63 - 7 (6 h) - 7 h^{2} - (3 + h)}{h}$

Step 1.5.2

Multiply $6$ by $- 7$ .

$\frac{- 5 - 63 - 42 h - 7 h^{2} - (3 + h)}{h}$

Step 1.6

Apply the distributive property.

$\frac{- 5 - 63 - 42 h - 7 h^{2} - 1 \cdot 3 - h}{h}$

Step 1.7

Multiply $- 1$ by $3$ .

$\frac{- 5 - 63 - 42 h - 7 h^{2} - 3 - h}{h}$

Step 1.8

Subtract $63$ from $- 5$ .

$\frac{- 68 - 42 h - 7 h^{2} - 3 - h}{h}$

Step 1.9

Subtract $3$ from $- 68$ .

$\frac{- 42 h - 7 h^{2} - 71 - h}{h}$

Step 1.10

Subtract $h$ from $- 42 h$ .

$\frac{- 43 h - 7 h^{2} - 71}{h}$

Step 1.11

Reorder terms.

$\frac{- 7 h^{2} - 43 h - 71}{h}$

Step 2

Simplify with factoring out.

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Step 2.1

Factor $- 1$ out of $- 7 h^{2}$ .

$\frac{- (7 h^{2}) - 43 h - 71}{h}$

Step 2.2

Factor $- 1$ out of $- 43 h$ .

$\frac{- (7 h^{2}) - (43 h) - 71}{h}$

Step 2.3

Factor $- 1$ out of $- (7 h^{2}) - (43 h)$ .

$\frac{- (7 h^{2} + 43 h) - 71}{h}$

Step 2.4

Rewrite $- 71$ as $- 1 (71)$ .

$\frac{- (7 h^{2} + 43 h) - 1 (71)}{h}$

Step 2.5

Factor $- 1$ out of $- (7 h^{2} + 43 h) - 1 (71)$ .

$\frac{- (7 h^{2} + 43 h + 71)}{h}$

Step 2.6

Simplify the expression.

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Step 2.6.1

Rewrite $- (7 h^{2} + 43 h + 71)$ as $- 1 (7 h^{2} + 43 h + 71)$ .

$\frac{- 1 (7 h^{2} + 43 h + 71)}{h}$

Step 2.6.2

Move the negative in front of the fraction.

$- \frac{7 h^{2} + 43 h + 71}{h}$