Basic Math Examples

$\frac{(- 3 - 6 {(h - 3)}^{2}) - (- 57)}{- 3 - h - (- 3)}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{- 3 - 6 ((h - 3) (h - 3)) - (- 57)}{- 3 - h - (- 3)}$

Step 1.2

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

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Step 1.2.1

Apply the distributive property.

$\frac{- 3 - 6 (h (h - 3) - 3 (h - 3)) - (- 57)}{- 3 - h - (- 3)}$

Step 1.2.2

Apply the distributive property.

$\frac{- 3 - 6 (h \cdot h + h \cdot - 3 - 3 (h - 3)) - (- 57)}{- 3 - h - (- 3)}$

Step 1.2.3

Apply the distributive property.

$\frac{- 3 - 6 (h \cdot h + h \cdot - 3 - 3 h - 3 \cdot - 3) - (- 57)}{- 3 - h - (- 3)}$

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 $h$ by $h$ .

$\frac{- 3 - 6 (h^{2} + h \cdot - 3 - 3 h - 3 \cdot - 3) - (- 57)}{- 3 - h - (- 3)}$

Step 1.3.1.2

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

$\frac{- 3 - 6 (h^{2} - 3 \cdot h - 3 h - 3 \cdot - 3) - (- 57)}{- 3 - h - (- 3)}$

Step 1.3.1.3

Multiply $- 3$ by $- 3$ .

$\frac{- 3 - 6 (h^{2} - 3 h - 3 h + 9) - (- 57)}{- 3 - h - (- 3)}$

Step 1.3.2

Subtract $3 h$ from $- 3 h$ .

$\frac{- 3 - 6 (h^{2} - 6 h + 9) - (- 57)}{- 3 - h - (- 3)}$

Step 1.4

Apply the distributive property.

$\frac{- 3 - 6 h^{2} - 6 (- 6 h) - 6 \cdot 9 - (- 57)}{- 3 - h - (- 3)}$

Step 1.5

Simplify.

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Step 1.5.1

Multiply $- 6$ by $- 6$ .

$\frac{- 3 - 6 h^{2} + 36 h - 6 \cdot 9 - (- 57)}{- 3 - h - (- 3)}$

Step 1.5.2

Multiply $- 6$ by $9$ .

$\frac{- 3 - 6 h^{2} + 36 h - 54 - (- 57)}{- 3 - h - (- 3)}$

Step 1.6

Multiply $- 1$ by $- 57$ .

$\frac{- 3 - 6 h^{2} + 36 h - 54 + 57}{- 3 - h - (- 3)}$

Step 1.7

Subtract $54$ from $- 3$ .

$\frac{- 6 h^{2} + 36 h - 57 + 57}{- 3 - h - (- 3)}$

Step 1.8

Add $- 57$ and $57$ .

$\frac{- 6 h^{2} + 36 h + 0}{- 3 - h - (- 3)}$

Step 1.9

Add $- 6 h^{2} + 36 h$ and $0$ .

$\frac{- 6 h^{2} + 36 h}{- 3 - h - (- 3)}$

Step 1.10

Factor $6 h$ out of $- 6 h^{2} + 36 h$ .

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Step 1.10.1

Factor $6 h$ out of $- 6 h^{2}$ .

$\frac{6 h (- h) + 36 h}{- 3 - h - (- 3)}$

Step 1.10.2

Factor $6 h$ out of $36 h$ .

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

Step 1.10.3

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

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

Step 2

Simplify the denominator.

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Step 2.1

Multiply $- 1$ by $- 3$ .

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

Step 2.2

Add $- 3$ and $3$ .

$\frac{6 h (- h + 6)}{- h + 0}$

Step 2.3

Add $- h$ and $0$ .

$\frac{6 h (- h + 6)}{- h}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $h$ .

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Step 3.1.1

Cancel the common factor.

$\frac{6 h (- h + 6)}{- h}$

Step 3.1.2

Rewrite the expression.

$\frac{6 (- h + 6)}{- 1}$

Step 3.1.3

Move the negative one from the denominator of $\frac{6 (- h + 6)}{- 1}$ .

$- 1 \cdot (6 (- h + 6))$

Step 3.2

Rewrite $- 1 \cdot (6 (- h + 6))$ as $- (6 (- h + 6))$ .

$- (6 (- h + 6))$

Step 3.3

Apply the distributive property.

$- (6 (- h) + 6 \cdot 6)$

Step 3.4

Multiply.

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Step 3.4.1

Multiply $- 1$ by $6$ .

$- (- 6 h + 6 \cdot 6)$

Step 3.4.2

Multiply $6$ by $6$ .

$- (- 6 h + 36)$

Step 3.5

Apply the distributive property.

$- (- 6 h) - 1 \cdot 36$

Step 3.6

Multiply.

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Step 3.6.1

Multiply $- 6$ by $- 1$ .

$6 h - 1 \cdot 36$

Step 3.6.2

Multiply $- 1$ by $36$ .

$6 h - 36$