Simplify (4x-1)/(3x^2y)-(7x-1)/(3x^2y)

$\frac{4 x - 1}{3 x^{2} y} - \frac{7 x - 1}{3 x^{2} y}$

Step 1

Combine the numerators over the common denominator.

$\frac{4 x - 1 - (7 x - 1)}{3 x^{2} y}$

Step 2

Simplify each term.

Apply the distributive property.

$\frac{4 x - 1 - (7 x) - - 1}{3 x^{2} y}$

Multiply $7$ by $- 1$ .

$\frac{4 x - 1 - 7 x - - 1}{3 x^{2} y}$

Multiply $- 1$ by $- 1$ .

$\frac{4 x - 1 - 7 x + 1}{3 x^{2} y}$

Step 3

Simplify terms.

Combine the opposite terms in $4 x - 1 - 7 x + 1$ .

Add $- 1$ and $1$ .

$\frac{4 x - 7 x + 0}{3 x^{2} y}$

Add $4 x - 7 x$ and $0$ .

$\frac{4 x - 7 x}{3 x^{2} y}$

Subtract $7 x$ from $4 x$ .

$\frac{- 3 x}{3 x^{2} y}$

Cancel the common factor of $- 3$ and $3$ .

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

$\frac{3 (- x)}{3 x^{2} y}$

Cancel the common factors.

Factor $3$ out of $3 x^{2} y$ .

$\frac{3 (- x)}{3 (x^{2} y)}$

Cancel the common factor.

$\frac{3 (- x)}{3 (x^{2} y)}$

Rewrite the expression.

$\frac{- x}{x^{2} y}$

Cancel the common factor of $x$ and $x^{2}$ .

Factor $x$ out of $- x$ .

$\frac{x \cdot - 1}{x^{2} y}$

Cancel the common factors.

Factor $x$ out of $x^{2} y$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{- 1}{x y}$

Move the negative in front of the fraction.

$- \frac{1}{x y}$