Simplify (2/x+6)/(1/y)

$\frac{\frac{2}{x} + 6}{\frac{1}{y}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(\frac{2}{x} + 6) y$

Step 2

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

$(\frac{2}{x} + \frac{6 x}{x}) y$

Step 3

Combine the numerators over the common denominator.

$\frac{2 + 6 x}{x} y$

Step 4

Factor $2$ out of $2 + 6 x$ .

Factor $2$ out of $2$ .

$\frac{2 (1) + 6 x}{x} y$

Factor $2$ out of $6 x$ .

$\frac{2 (1) + 2 (3 x)}{x} y$

Factor $2$ out of $2 (1) + 2 (3 x)$ .

$\frac{2 (1 + 3 x)}{x} y$

Step 5

Combine $\frac{2 (1 + 3 x)}{x}$ and $y$ .

$\frac{2 (1 + 3 x) y}{x}$

Step 6

Reorder factors in $\frac{2 (1 + 3 x) y}{x}$ .

$\frac{2 y (1 + 3 x)}{x}$