Algebra Examples

$\frac{n + 6}{10 n + 4} + \frac{2 n}{3}$

Step 1

Factor $2$ out of $10 n + 4$ .

Tap for more steps...

Step 1.1

Factor $2$ out of $10 n$ .

$\frac{n + 6}{2 (5 n) + 4} + \frac{2 n}{3}$

Step 1.2

Factor $2$ out of $4$ .

$\frac{n + 6}{2 (5 n) + 2 (2)} + \frac{2 n}{3}$

Step 1.3

Factor $2$ out of $2 (5 n) + 2 (2)$ .

$\frac{n + 6}{2 (5 n + 2)} + \frac{2 n}{3}$

Step 2

To write $\frac{n + 6}{2 (5 n + 2)}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{n + 6}{2 (5 n + 2)} \cdot \frac{3}{3} + \frac{2 n}{3}$

Step 3

To write $\frac{2 n}{3}$ as a fraction with a common denominator, multiply by $\frac{2 (5 n + 2)}{2 (5 n + 2)}$ .

$\frac{n + 6}{2 (5 n + 2)} \cdot \frac{3}{3} + \frac{2 n}{3} \cdot \frac{2 (5 n + 2)}{2 (5 n + 2)}$

Step 4

Write each expression with a common denominator of $6 (5 n + 2)$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 4.1

Multiply $\frac{n + 6}{2 (5 n + 2)}$ by $\frac{3}{3}$ .

$\frac{(n + 6) \cdot 3}{2 (5 n + 2) \cdot 3} + \frac{2 n}{3} \cdot \frac{2 (5 n + 2)}{2 (5 n + 2)}$

Step 4.2

Multiply $3$ by $2$ .

$\frac{(n + 6) \cdot 3}{6 (5 n + 2)} + \frac{2 n}{3} \cdot \frac{2 (5 n + 2)}{2 (5 n + 2)}$

Step 4.3

Multiply $\frac{2 n}{3}$ by $\frac{2 (5 n + 2)}{2 (5 n + 2)}$ .

$\frac{(n + 6) \cdot 3}{6 (5 n + 2)} + \frac{2 n (2 (5 n + 2))}{3 (2 (5 n + 2))}$

Step 4.4

Multiply $2$ by $3$ .

$\frac{(n + 6) \cdot 3}{6 (5 n + 2)} + \frac{2 n (2 (5 n + 2))}{6 (5 n + 2)}$

Step 5

Combine the numerators over the common denominator.

$\frac{(n + 6) \cdot 3 + 2 n (2 (5 n + 2))}{6 (5 n + 2)}$

Step 6

Simplify the numerator.

Tap for more steps...

Step 6.1

Apply the distributive property.

$\frac{n \cdot 3 + 6 \cdot 3 + 2 n (2 (5 n + 2))}{6 (5 n + 2)}$

Step 6.2

Move $3$ to the left of $n$ .

$\frac{3 \cdot n + 6 \cdot 3 + 2 n (2 (5 n + 2))}{6 (5 n + 2)}$

Step 6.3

Multiply $6$ by $3$ .

$\frac{3 \cdot n + 18 + 2 n (2 (5 n + 2))}{6 (5 n + 2)}$

Step 6.4

Apply the distributive property.

$\frac{3 n + 18 + 2 n (2 (5 n) + 2 \cdot 2)}{6 (5 n + 2)}$

Step 6.5

Multiply $5$ by $2$ .

$\frac{3 n + 18 + 2 n (10 n + 2 \cdot 2)}{6 (5 n + 2)}$

Step 6.6

Multiply $2$ by $2$ .

$\frac{3 n + 18 + 2 n (10 n + 4)}{6 (5 n + 2)}$

Step 6.7

Apply the distributive property.

$\frac{3 n + 18 + 2 n (10 n) + 2 n \cdot 4}{6 (5 n + 2)}$

Step 6.8

Rewrite using the commutative property of multiplication.

$\frac{3 n + 18 + 2 \cdot 10 n \cdot n + 2 n \cdot 4}{6 (5 n + 2)}$

Step 6.9

Multiply $4$ by $2$ .

$\frac{3 n + 18 + 2 \cdot 10 n \cdot n + 8 n}{6 (5 n + 2)}$

Step 6.10

Simplify each term.

Tap for more steps...

Step 6.10.1

Multiply $n$ by $n$ by adding the exponents.

Tap for more steps...

Step 6.10.1.1

Move $n$ .

$\frac{3 n + 18 + 2 \cdot 10 (n \cdot n) + 8 n}{6 (5 n + 2)}$

Step 6.10.1.2

Multiply $n$ by $n$ .

$\frac{3 n + 18 + 2 \cdot 10 n^{2} + 8 n}{6 (5 n + 2)}$

Step 6.10.2

Multiply $2$ by $10$ .

$\frac{3 n + 18 + 20 n^{2} + 8 n}{6 (5 n + 2)}$

Step 6.11

Add $3 n$ and $8 n$ .

$\frac{11 n + 18 + 20 n^{2}}{6 (5 n + 2)}$

Step 6.12

Reorder terms.

$\frac{20 n^{2} + 11 n + 18}{6 (5 n + 2)}$