Evaluate 2/(ac)+1/(ab)+3/(bc)

$\frac{2}{a c} + \frac{1}{a b} + \frac{3}{b c}$

Step 1

To write $\frac{2}{a c}$ as a fraction with a common denominator, multiply by $\frac{b}{b}$ .

$\frac{2}{a c} \cdot \frac{b}{b} + \frac{1}{a b} + \frac{3}{b c}$

Step 2

To write $\frac{1}{a b}$ as a fraction with a common denominator, multiply by $\frac{c}{c}$ .

$\frac{2}{a c} \cdot \frac{b}{b} + \frac{1}{a b} \cdot \frac{c}{c} + \frac{3}{b c}$

Step 3

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

Multiply $\frac{2}{a c}$ by $\frac{b}{b}$ .

$\frac{2 b}{a c b} + \frac{1}{a b} \cdot \frac{c}{c} + \frac{3}{b c}$

Multiply $\frac{1}{a b}$ by $\frac{c}{c}$ .

$\frac{2 b}{a c b} + \frac{c}{a b c} + \frac{3}{b c}$

Reorder the factors of $a c b$ .

$\frac{2 b}{a b c} + \frac{c}{a b c} + \frac{3}{b c}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 b + c}{a b c} + \frac{3}{b c}$

Step 5

To write $\frac{3}{b c}$ as a fraction with a common denominator, multiply by $\frac{a}{a}$ .

$\frac{2 b + c}{a b c} + \frac{3}{b c} \cdot \frac{a}{a}$

Step 6

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

Multiply $\frac{3}{b c}$ by $\frac{a}{a}$ .

$\frac{2 b + c}{a b c} + \frac{3 a}{b c a}$

Reorder the factors of $b c a$ .

$\frac{2 b + c}{a b c} + \frac{3 a}{a b c}$

Step 7

Combine the numerators over the common denominator.

$\frac{2 b + c + 3 a}{a b c}$