Simplify (-y+6/x)/(-(5y)/x)

$\frac{- y + \frac{6}{x}}{- \frac{5 y}{x}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(- y + \frac{6}{x}) (- \frac{x}{5 y})$

Step 2

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

$(- y \cdot \frac{x}{x} + \frac{6}{x}) (- \frac{x}{5 y})$

Step 3

Combine $- y$ and $\frac{x}{x}$ .

$(\frac{- y x}{x} + \frac{6}{x}) (- \frac{x}{5 y})$

Step 4

Combine the numerators over the common denominator.

$\frac{- y x + 6}{x} (- \frac{x}{5 y})$

Step 5

Rewrite using the commutative property of multiplication.

$- \frac{- y x + 6}{x} \cdot \frac{x}{5 y}$

Step 6

Cancel the common factor of $x$ .

Move the leading negative in $- \frac{- y x + 6}{x}$ into the numerator.

$\frac{- (- y x + 6)}{x} \cdot \frac{x}{5 y}$

Cancel the common factor.

$\frac{- (- y x + 6)}{x} \cdot \frac{x}{5 y}$

Rewrite the expression.

$- (- y x + 6) \frac{1}{5 y}$

Step 7

Apply the distributive property.

$(- (- y x) - 1 \cdot 6) \frac{1}{5 y}$

Step 8

Multiply $- (- y x)$ .

Multiply $- 1$ by $- 1$ .

$(1 (y x) - 1 \cdot 6) \frac{1}{5 y}$

Multiply $y$ by $1$ .

$(y x - 1 \cdot 6) \frac{1}{5 y}$

Step 9

Multiply $- 1$ by $6$ .

$(y x - 6) \frac{1}{5 y}$

Step 10

Multiply $y x - 6$ by $\frac{1}{5 y}$ .

$\frac{y x - 6}{5 y}$