Simplify (x-4y)/(12x)-(4x+5y)/(12x)

$\frac{x - 4 y}{12 x} - \frac{4 x + 5 y}{12 x}$

Step 1

Combine the numerators over the common denominator.

$\frac{x - 4 y - (4 x + 5 y)}{12 x}$

Step 2

Simplify each term.

Apply the distributive property.

$\frac{x - 4 y - (4 x) - (5 y)}{12 x}$

Multiply $4$ by $- 1$ .

$\frac{x - 4 y - 4 x - (5 y)}{12 x}$

Multiply $5$ by $- 1$ .

$\frac{x - 4 y - 4 x - 5 y}{12 x}$

Step 3

Simplify terms.

Subtract $4 x$ from $x$ .

$\frac{- 3 x - 4 y - 5 y}{12 x}$

Subtract $5 y$ from $- 4 y$ .

$\frac{- 3 x - 9 y}{12 x}$

Cancel the common factor of $- 3 x - 9 y$ and $12$ .

Factor $3$ out of $- 3 x$ .

$\frac{3 (- x) - 9 y}{12 x}$

Factor $3$ out of $- 9 y$ .

$\frac{3 (- x) + 3 (- 3 y)}{12 x}$

Factor $3$ out of $3 (- x) + 3 (- 3 y)$ .

$\frac{3 (- x - 3 y)}{12 x}$

Cancel the common factors.

Factor $3$ out of $12 x$ .

$\frac{3 (- x - 3 y)}{3 (4 x)}$

Cancel the common factor.

$\frac{3 (- x - 3 y)}{3 (4 x)}$

Rewrite the expression.

$\frac{- x - 3 y}{4 x}$

Factor $- 1$ out of $- x$ .

$\frac{- (x) - 3 y}{4 x}$

Factor $- 1$ out of $- 3 y$ .

$\frac{- (x) - (3 y)}{4 x}$

Factor $- 1$ out of $- (x) - (3 y)$ .

$\frac{- (x + 3 y)}{4 x}$

Simplify the expression.

Rewrite $- (x + 3 y)$ as $- 1 (x + 3 y)$ .

$\frac{- 1 (x + 3 y)}{4 x}$

Move the negative in front of the fraction.

$- \frac{x + 3 y}{4 x}$