Simplify (5n+1)/6+(3n-2)/8

$\frac{5 n + 1}{6} + \frac{3 n - 2}{8}$

Step 1

To write $\frac{5 n + 1}{6}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{5 n + 1}{6} \cdot \frac{4}{4} + \frac{3 n - 2}{8}$

Step 2

To write $\frac{3 n - 2}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5 n + 1}{6} \cdot \frac{4}{4} + \frac{3 n - 2}{8} \cdot \frac{3}{3}$

Step 3

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5 n + 1}{6}$ by $\frac{4}{4}$ .

$\frac{(5 n + 1) \cdot 4}{6 \cdot 4} + \frac{3 n - 2}{8} \cdot \frac{3}{3}$

Multiply $6$ by $4$ .

$\frac{(5 n + 1) \cdot 4}{24} + \frac{3 n - 2}{8} \cdot \frac{3}{3}$

Multiply $\frac{3 n - 2}{8}$ by $\frac{3}{3}$ .

$\frac{(5 n + 1) \cdot 4}{24} + \frac{(3 n - 2) \cdot 3}{8 \cdot 3}$

Multiply $8$ by $3$ .

$\frac{(5 n + 1) \cdot 4}{24} + \frac{(3 n - 2) \cdot 3}{24}$

Step 4

Combine the numerators over the common denominator.

$\frac{(5 n + 1) \cdot 4 + (3 n - 2) \cdot 3}{24}$

Step 5

Simplify the numerator.

Apply the distributive property.

$\frac{5 n \cdot 4 + 1 \cdot 4 + (3 n - 2) \cdot 3}{24}$

Multiply $4$ by $5$ .

$\frac{20 n + 1 \cdot 4 + (3 n - 2) \cdot 3}{24}$

Multiply $4$ by $1$ .

$\frac{20 n + 4 + (3 n - 2) \cdot 3}{24}$

Apply the distributive property.

$\frac{20 n + 4 + 3 n \cdot 3 - 2 \cdot 3}{24}$

Multiply $3$ by $3$ .

$\frac{20 n + 4 + 9 n - 2 \cdot 3}{24}$

Multiply $- 2$ by $3$ .

$\frac{20 n + 4 + 9 n - 6}{24}$

Add $20 n$ and $9 n$ .

$\frac{29 n + 4 - 6}{24}$

Subtract $6$ from $4$ .

$\frac{29 n - 2}{24}$