Simplify 1/(7x)+5/(6x)

$\frac{1}{7 x} + \frac{5}{6 x}$

Step 1

To write $\frac{1}{7 x}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{1}{7 x} \cdot \frac{6}{6} + \frac{5}{6 x}$

Step 2

To write $\frac{5}{6 x}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{1}{7 x} \cdot \frac{6}{6} + \frac{5}{6 x} \cdot \frac{7}{7}$

Step 3

Write each expression with a common denominator of $42 x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{7 x}$ by $\frac{6}{6}$ .

$\frac{6}{7 x \cdot 6} + \frac{5}{6 x} \cdot \frac{7}{7}$

Multiply $6$ by $7$ .

$\frac{6}{42 x} + \frac{5}{6 x} \cdot \frac{7}{7}$

Multiply $\frac{5}{6 x}$ by $\frac{7}{7}$ .

$\frac{6}{42 x} + \frac{5 \cdot 7}{6 x \cdot 7}$

Multiply $7$ by $6$ .

$\frac{6}{42 x} + \frac{5 \cdot 7}{42 x}$

Step 4

Combine the numerators over the common denominator.

$\frac{6 + 5 \cdot 7}{42 x}$

Step 5

Simplify the numerator.

Multiply $5$ by $7$ .

$\frac{6 + 35}{42 x}$

Add $6$ and $35$ .

$\frac{41}{42 x}$