Simplify (1/3+1/5-1/7)/(1/x)

$\frac{\frac{1}{3} + \frac{1}{5} - \frac{1}{7}}{\frac{1}{x}}$

Multiply the numerator by the reciprocal of the denominator.

$(\frac{1}{3} + \frac{1}{5} - \frac{1}{7}) x$

Find the common denominator.

Multiply $\frac{1}{3}$ by $\frac{35}{35}$ .

$(\frac{1}{3} \cdot \frac{35}{35} + \frac{1}{5} - \frac{1}{7}) x$

Multiply $\frac{1}{3}$ by $\frac{35}{35}$ .

$(\frac{35}{3 \cdot 35} + \frac{1}{5} - \frac{1}{7}) x$

Multiply $\frac{1}{5}$ by $\frac{21}{21}$ .

$(\frac{35}{3 \cdot 35} + \frac{1}{5} \cdot \frac{21}{21} - \frac{1}{7}) x$

Multiply $\frac{1}{5}$ by $\frac{21}{21}$ .

$(\frac{35}{3 \cdot 35} + \frac{21}{5 \cdot 21} - \frac{1}{7}) x$

Multiply $\frac{1}{7}$ by $\frac{15}{15}$ .

$(\frac{35}{3 \cdot 35} + \frac{21}{5 \cdot 21} - (\frac{1}{7} \cdot \frac{15}{15})) x$

Multiply $\frac{1}{7}$ by $\frac{15}{15}$ .

$(\frac{35}{3 \cdot 35} + \frac{21}{5 \cdot 21} - \frac{15}{7 \cdot 15}) x$

Multiply $3$ by $35$ .

$(\frac{35}{105} + \frac{21}{5 \cdot 21} - \frac{15}{7 \cdot 15}) x$

Multiply $5$ by $21$ .

$(\frac{35}{105} + \frac{21}{105} - \frac{15}{7 \cdot 15}) x$

Multiply $7$ by $15$ .

$(\frac{35}{105} + \frac{21}{105} - \frac{15}{105}) x$

Combine the numerators over the common denominator.

$\frac{35 + 21 - 15}{105} x$

Simplify by adding and subtracting.

Add $35$ and $21$ .

$\frac{56 - 15}{105} x$

Subtract $15$ from $56$ .

$\frac{41}{105} x$

Combine $\frac{41}{105}$ and $x$ .

$\frac{41 x}{105}$