Simplify -7/(5x)+(x+4)/x

$\frac{- 7}{5 x} + \frac{x + 4}{x}$

Step 1

Move the negative in front of the fraction.

$- \frac{7}{5 x} + \frac{x + 4}{x}$

Step 2

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

$- \frac{7}{5 x} + \frac{x + 4}{x} \cdot \frac{5}{5}$

Step 3

Write each expression with a common denominator of $5 x$ , by multiplying each by an appropriate factor of $1$ .

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

$- \frac{7}{5 x} + \frac{(x + 4) \cdot 5}{x \cdot 5}$

Reorder the factors of $x \cdot 5$ .

$- \frac{7}{5 x} + \frac{(x + 4) \cdot 5}{5 x}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 7 + (x + 4) \cdot 5}{5 x}$

Step 5

Simplify the numerator.

Apply the distributive property.

$\frac{- 7 + x \cdot 5 + 4 \cdot 5}{5 x}$

Move $5$ to the left of $x$ .

$\frac{- 7 + 5 \cdot x + 4 \cdot 5}{5 x}$

Multiply $4$ by $5$ .

$\frac{- 7 + 5 \cdot x + 20}{5 x}$

Add $- 7$ and $20$ .

$\frac{5 x + 13}{5 x}$