Basic Math Examples

$\frac{\frac{9}{1 + h} - \frac{9}{1}}{h}$

Step 1

Divide $9$ by $1$ .

$\frac{\frac{9}{1 + h} - 1 \cdot 9}{h}$

Step 2

Simplify the numerator.

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Step 2.1

Multiply $- 1$ by $9$ .

$\frac{\frac{9}{1 + h} - 9}{h}$

Step 2.2

To write $- 9$ as a fraction with a common denominator, multiply by $\frac{1 + h}{1 + h}$ .

$\frac{\frac{9}{1 + h} - 9 \cdot \frac{1 + h}{1 + h}}{h}$

Step 2.3

Combine $- 9$ and $\frac{1 + h}{1 + h}$ .

$\frac{\frac{9}{1 + h} + \frac{- 9 (1 + h)}{1 + h}}{h}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{\frac{9 - 9 (1 + h)}{1 + h}}{h}$

Step 2.5

Reorder terms.

$\frac{\frac{9 - 9 (1 + h)}{h + 1}}{h}$

Step 2.6

Rewrite $\frac{9 - 9 (1 + h)}{h + 1}$ in a factored form.

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Step 2.6.1

Factor $9$ out of $9 - 9 (1 + h)$ .

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Step 2.6.1.1

Factor $9$ out of $9$ .

$\frac{\frac{9 (1) - 9 (1 + h)}{h + 1}}{h}$

Step 2.6.1.2

Factor $9$ out of $- 9 (1 + h)$ .

$\frac{\frac{9 (1) + 9 (- (1 + h))}{h + 1}}{h}$

Step 2.6.1.3

Factor $9$ out of $9 (1) + 9 (- (1 + h))$ .

$\frac{\frac{9 (1 - (1 + h))}{h + 1}}{h}$

Step 2.6.2

Apply the distributive property.

$\frac{\frac{9 (1 - 1 \cdot 1 - h)}{h + 1}}{h}$

Step 2.6.3

Multiply $- 1$ by $1$ .

$\frac{\frac{9 (1 - 1 - h)}{h + 1}}{h}$

Step 2.6.4

Subtract $1$ from $1$ .

$\frac{\frac{9 (0 - h)}{h + 1}}{h}$

Step 2.6.5

Subtract $h$ from $0$ .

$\frac{\frac{9 \cdot - 1 h}{h + 1}}{h}$

Step 2.6.6

Combine exponents.

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Step 2.6.6.1

Factor out negative.

$\frac{\frac{- (9 h)}{h + 1}}{h}$

Step 2.6.6.2

Multiply $9$ by $- 1$ .

$\frac{\frac{- 9 h}{h + 1}}{h}$

Step 2.7

Move the negative in front of the fraction.

$\frac{- \frac{9 h}{h + 1}}{h}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$- \frac{9 h}{h + 1} \cdot \frac{1}{h}$

Step 4

Cancel the common factor of $h$ .

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Step 4.1

Move the leading negative in $- \frac{9 h}{h + 1}$ into the numerator.

$\frac{- 9 h}{h + 1} \cdot \frac{1}{h}$

Step 4.2

Factor $h$ out of $- 9 h$ .

$\frac{h \cdot - 9}{h + 1} \cdot \frac{1}{h}$

Step 4.3

Cancel the common factor.

$\frac{h \cdot - 9}{h + 1} \cdot \frac{1}{h}$

Step 4.4

Rewrite the expression.

$\frac{- 9}{h + 1}$

Step 5

Move the negative in front of the fraction.

$- \frac{9}{h + 1}$