Basic Math Examples

$\frac{(61 (1 + h) - 0.83 {(1 + h)}^{2}) - 60.17}{h}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $0.01$ out of $61 (1 + h) - 0.83 {(1 + h)}^{2} - 60.17$ .

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Step 1.1.1

Reorder the expression.

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Step 1.1.1.1

Reorder $1$ and $h$ .

$\frac{61 (h + 1) - 0.83 {(1 + h)}^{2} - 60.17}{h}$

Step 1.1.1.2

Reorder $1$ and $h$ .

$\frac{61 (h + 1) - 0.83 {(h + 1)}^{2} - 60.17}{h}$

Step 1.1.2

Factor $0.01$ out of $61 (h + 1)$ .

$\frac{0.01 (6100 (h + 1)) - 0.83 {(h + 1)}^{2} - 60.17}{h}$

Step 1.1.3

Factor $0.01$ out of $- 0.83 {(h + 1)}^{2}$ .

$\frac{0.01 (6100 (h + 1)) + 0.01 (- 83 {(h + 1)}^{2}) - 60.17}{h}$

Step 1.1.4

Factor $0.01$ out of $- 60.17$ .

$\frac{0.01 (6100 (h + 1)) + 0.01 (- 83 {(h + 1)}^{2}) + 0.01 (- 6017)}{h}$

Step 1.1.5

Factor $0.01$ out of $0.01 (6100 (h + 1)) + 0.01 (- 83 {(h + 1)}^{2})$ .

$\frac{0.01 (6100 (h + 1) - 83 {(h + 1)}^{2}) + 0.01 (- 6017)}{h}$

Step 1.1.6

Factor $0.01$ out of $0.01 (6100 (h + 1) - 83 {(h + 1)}^{2}) + 0.01 (- 6017)$ .

$\frac{0.01 (6100 (h + 1) - 83 {(h + 1)}^{2} - 6017)}{h}$

Step 1.2

Let $u = h + 1$ . Substitute $u$ for all occurrences of $h + 1$ .

$\frac{0.01 (6100 u - 83 u^{2} - 6017)}{h}$

Step 1.3

Factor by grouping.

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Step 1.3.1

Reorder terms.

$\frac{0.01 (- 83 u^{2} + 6100 u - 6017)}{h}$

Step 1.3.2

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = - 83 \cdot - 6017 = 499411$ and whose sum is $b = 6100$ .

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Step 1.3.2.1

Factor $6100$ out of $6100 u$ .

$\frac{0.01 (- 83 u^{2} + 6100 (u) - 6017)}{h}$

Step 1.3.2.2

Rewrite $6100$ as $83$ plus $6017$

$\frac{0.01 (- 83 u^{2} + (83 + 6017) u - 6017)}{h}$

Step 1.3.2.3

Apply the distributive property.

$\frac{0.01 (- 83 u^{2} + 83 u + 6017 u - 6017)}{h}$

Step 1.3.3

Factor out the greatest common factor from each group.

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Step 1.3.3.1

Group the first two terms and the last two terms.

$\frac{0.01 ((- 83 u^{2} + 83 u) + 6017 u - 6017)}{h}$

Step 1.3.3.2

Factor out the greatest common factor (GCF) from each group.

$\frac{0.01 (83 u (- u + 1) - 6017 (- u + 1))}{h}$

Step 1.3.4

Factor the polynomial by factoring out the greatest common factor, $- u + 1$ .

$\frac{0.01 ((- u + 1) (83 u - 6017))}{h}$

Step 1.4

Replace all occurrences of $u$ with $h + 1$ .

$\frac{0.01 ((- (h + 1) + 1) (83 (h + 1) - 6017))}{h}$

Step 1.5

Simplify.

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Step 1.5.1

Simplify each term.

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Step 1.5.1.1

Apply the distributive property.

$\frac{0.01 ((- h - 1 \cdot 1 + 1) (83 (h + 1) - 6017))}{h}$

Step 1.5.1.2

Multiply $- 1$ by $1$ .

$\frac{0.01 ((- h - 1 + 1) (83 (h + 1) - 6017))}{h}$

Step 1.5.2

Combine the opposite terms in $- h - 1 + 1$ .

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Step 1.5.2.1

Add $- 1$ and $1$ .

$\frac{0.01 ((- h + 0) (83 (h + 1) - 6017))}{h}$

Step 1.5.2.2

Add $- h$ and $0$ .

$\frac{0.01 (- h (83 (h + 1) - 6017))}{h}$

Step 1.5.3

Simplify each term.

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Step 1.5.3.1

Apply the distributive property.

$\frac{0.01 (- h (83 h + 83 \cdot 1 - 6017))}{h}$

Step 1.5.3.2

Multiply $83$ by $1$ .

$\frac{0.01 (- h (83 h + 83 - 6017))}{h}$

Step 1.5.4

Subtract $6017$ from $83$ .

$\frac{0.01 (- h (83 h - 5934))}{h}$

$\frac{0.01 \cdot - 1 h (83 h - 5934)}{h}$

Step 1.6

Combine exponents.

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Step 1.6.1

Factor out negative.

$\frac{- (0.01 h (83 h - 5934))}{h}$

Step 1.6.2

Multiply $0.01$ by $- 1$ .

$\frac{- 0.01 (h (83 h - 5934))}{h}$

$\frac{- 0.01 h (83 h - 5934)}{h}$

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.

$\frac{- 0.01 h (83 h - 5934)}{h}$

Step 2.1.2

Divide $- 0.01 (83 h - 5934)$ by $1$ .

$- 0.01 (83 h - 5934)$

Step 2.2

Apply the distributive property.

$- 0.01 (83 h) - 0.01 \cdot - 5934$

Step 2.3

Multiply.

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Step 2.3.1

Multiply $83$ by $- 0.01$ .

$- 0.83 h - 0.01 \cdot - 5934$

Step 2.3.2

Multiply $- 0.01$ by $- 5934$ .

$- 0.83 h + 59.34$