Basic Math Examples

$\frac{n + 2}{3} + \frac{n}{3 n - 6}$

Step 1

Factor $3$ out of $3 n - 6$ .

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Step 1.1

Factor $3$ out of $3 n$ .

$\frac{n + 2}{3} + \frac{n}{3 (n) - 6}$

Step 1.2

Factor $3$ out of $- 6$ .

$\frac{n + 2}{3} + \frac{n}{3 n + 3 \cdot - 2}$

Step 1.3

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

$\frac{n + 2}{3} + \frac{n}{3 (n - 2)}$

Step 2

To write $\frac{n + 2}{3}$ as a fraction with a common denominator, multiply by $\frac{n - 2}{n - 2}$ .

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

Step 3

Simplify terms.

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Step 3.1

Multiply $\frac{n + 2}{3}$ by $\frac{n - 2}{n - 2}$ .

$\frac{(n + 2) (n - 2)}{3 (n - 2)} + \frac{n}{3 (n - 2)}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{(n + 2) (n - 2) + n}{3 (n - 2)}$

Step 4

Simplify the numerator.

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Step 4.1

Expand $(n + 2) (n - 2)$ using the FOIL Method.

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Step 4.1.1

Apply the distributive property.

$\frac{n (n - 2) + 2 (n - 2) + n}{3 (n - 2)}$

Step 4.1.2

Apply the distributive property.

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

Step 4.1.3

Apply the distributive property.

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

Step 4.2

Combine the opposite terms in $n \cdot n + n \cdot - 2 + 2 n + 2 \cdot - 2$ .

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Step 4.2.1

Reorder the factors in the terms $n \cdot - 2$ and $2 n$ .

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

Step 4.2.2

Add $- 2 n$ and $2 n$ .

$\frac{n \cdot n + 0 + 2 \cdot - 2 + n}{3 (n - 2)}$

Step 4.2.3

Add $n \cdot n$ and $0$ .

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

Step 4.3

Simplify each term.

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Step 4.3.1

Multiply $n$ by $n$ .

$\frac{n^{2} + 2 \cdot - 2 + n}{3 (n - 2)}$

Step 4.3.2

Multiply $2$ by $- 2$ .

$\frac{n^{2} - 4 + n}{3 (n - 2)}$

Step 4.4

Reorder terms.

$\frac{n^{2} + n - 4}{3 (n - 2)}$