Basic Math Examples

$9 + \frac{9}{3 - 6 + 9}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $9$ and $3 - 6 + 9$ .

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Step 1.1.1

Factor $3$ out of $9$ .

$9 + \frac{3 \cdot 3}{3 - 6 + 9}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $3$ out of $3$ .

$9 + \frac{3 \cdot 3}{3 (1) - 6 + 9}$

Step 1.1.2.2

Factor $3$ out of $- 6$ .

$9 + \frac{3 \cdot 3}{3 \cdot 1 + 3 \cdot - 2 + 9}$

Step 1.1.2.3

Factor $3$ out of $3 \cdot 1 + 3 \cdot - 2$ .

$9 + \frac{3 \cdot 3}{3 \cdot (1 - 2) + 9}$

Step 1.1.2.4

Factor $3$ out of $9$ .

$9 + \frac{3 \cdot 3}{3 \cdot (1 - 2) + 3 (3)}$

Step 1.1.2.5

Factor $3$ out of $3 \cdot (1 - 2) + 3 (3)$ .

$9 + \frac{3 \cdot 3}{3 \cdot (1 - 2 + 3)}$

Step 1.1.2.6

Cancel the common factor.

$9 + \frac{3 \cdot 3}{3 \cdot (1 - 2 + 3)}$

Step 1.1.2.7

Rewrite the expression.

$9 + \frac{3}{1 - 2 + 3}$

Step 1.2

Simplify the denominator.

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Step 1.2.1

Subtract $2$ from $1$ .

$9 + \frac{3}{- 1 + 3}$

Step 1.2.2

Add $- 1$ and $3$ .

$9 + \frac{3}{2}$

Step 2

To write $9$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$9 \cdot \frac{2}{2} + \frac{3}{2}$

Step 3

Combine $9$ and $\frac{2}{2}$ .

$\frac{9 \cdot 2}{2} + \frac{3}{2}$

Step 4

Combine the numerators over the common denominator.

$\frac{9 \cdot 2 + 3}{2}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $9$ by $2$ .

$\frac{18 + 3}{2}$

Step 5.2

Add $18$ and $3$ .

$\frac{21}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{21}{2}$

Decimal Form:

$10.5$

Mixed Number Form:

$10 \frac{1}{2}$