Algebra Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Find the common denominator.

Tap for more steps...

Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

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

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

Step 2.5

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

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

Step 2.6

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

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

Step 2.7

Multiply $3$ by $35$ .

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

Step 2.8

Multiply $5$ by $21$ .

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

Step 2.9

Multiply $7$ by $15$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify by adding and subtracting.

Tap for more steps...

Step 4.1

Add $35$ and $21$ .

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

Step 4.2

Subtract $15$ from $56$ .

$\frac{41}{105} x$

Step 5

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

$\frac{41 x}{105}$