Simplify (5x+1)/(5x)-(4x+1)/(4x)

$\frac{5 x + 1}{5 x} - \frac{4 x + 1}{4 x}$

To write $\frac{5 x + 1}{5 x}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{5 x + 1}{5 x} \cdot \frac{4}{4} - \frac{4 x + 1}{4 x}$

To write $- \frac{4 x + 1}{4 x}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{5 x + 1}{5 x} \cdot \frac{4}{4} - \frac{4 x + 1}{4 x} \cdot \frac{5}{5}$

Write each expression with a common denominator of $20 x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5 x + 1}{5 x}$ by $\frac{4}{4}$ .

$\frac{(5 x + 1) \cdot 4}{5 x \cdot 4} - \frac{4 x + 1}{4 x} \cdot \frac{5}{5}$

Multiply $4$ by $5$ .

$\frac{(5 x + 1) \cdot 4}{20 x} - \frac{4 x + 1}{4 x} \cdot \frac{5}{5}$

Multiply $\frac{4 x + 1}{4 x}$ by $\frac{5}{5}$ .

$\frac{(5 x + 1) \cdot 4}{20 x} - \frac{(4 x + 1) \cdot 5}{4 x \cdot 5}$

Multiply $5$ by $4$ .

$\frac{(5 x + 1) \cdot 4}{20 x} - \frac{(4 x + 1) \cdot 5}{20 x}$

Combine the numerators over the common denominator.

$\frac{(5 x + 1) \cdot 4 - (4 x + 1) \cdot 5}{20 x}$

Simplify the numerator.

Apply the distributive property.

$\frac{5 x \cdot 4 + 1 \cdot 4 - (4 x + 1) \cdot 5}{20 x}$

Multiply $4$ by $5$ .

$\frac{20 x + 1 \cdot 4 - (4 x + 1) \cdot 5}{20 x}$

Multiply $4$ by $1$ .

$\frac{20 x + 4 - (4 x + 1) \cdot 5}{20 x}$

Apply the distributive property.

$\frac{20 x + 4 + (- (4 x) - 1 \cdot 1) \cdot 5}{20 x}$

Multiply $4$ by $- 1$ .

$\frac{20 x + 4 + (- 4 x - 1 \cdot 1) \cdot 5}{20 x}$

Multiply $- 1$ by $1$ .

$\frac{20 x + 4 + (- 4 x - 1) \cdot 5}{20 x}$

Apply the distributive property.

$\frac{20 x + 4 - 4 x \cdot 5 - 1 \cdot 5}{20 x}$

Multiply $5$ by $- 4$ .

$\frac{20 x + 4 - 20 x - 1 \cdot 5}{20 x}$

Multiply $- 1$ by $5$ .

$\frac{20 x + 4 - 20 x - 5}{20 x}$

Subtract $20 x$ from $20 x$ .

$\frac{0 + 4 - 5}{20 x}$

Add $0$ and $4$ .

$\frac{4 - 5}{20 x}$

Subtract $5$ from $4$ .

$\frac{- 1}{20 x}$

Move the negative in front of the fraction.

$- \frac{1}{20 x}$