Simplify (2ab)/c-(13b)/(11a)

$\frac{2 a b}{c} - \frac{13 b}{11 a}$

Step 1

To write $\frac{2 a b}{c}$ as a fraction with a common denominator, multiply by $\frac{11 a}{11 a}$ .

$\frac{2 a b}{c} \cdot \frac{11 a}{11 a} - \frac{13 b}{11 a}$

Step 2

To write $- \frac{13 b}{11 a}$ as a fraction with a common denominator, multiply by $\frac{c}{c}$ .

$\frac{2 a b}{c} \cdot \frac{11 a}{11 a} - \frac{13 b}{11 a} \cdot \frac{c}{c}$

Step 3

Write each expression with a common denominator of $c \cdot 11 a$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2 a b}{c}$ by $\frac{11 a}{11 a}$ .

$\frac{2 a b (11 a)}{c (11 a)} - \frac{13 b}{11 a} \cdot \frac{c}{c}$

Multiply $\frac{13 b}{11 a}$ by $\frac{c}{c}$ .

$\frac{2 a b (11 a)}{c (11 a)} - \frac{13 b c}{11 a c}$

Reorder the factors of $c (11 a)$ .

$\frac{2 a b (11 a)}{11 a c} - \frac{13 b c}{11 a c}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 a b (11 a) - 13 b c}{11 a c}$

Step 5

Simplify the numerator.

Factor $b$ out of $2 a b (11 a) - 13 b c$ .

Factor $b$ out of $2 a b (11 a)$ .

$\frac{b (2 a (11 a)) - 13 b c}{11 a c}$

Factor $b$ out of $- 13 b c$ .

$\frac{b (2 a (11 a)) + b (- 13 c)}{11 a c}$

Factor $b$ out of $b (2 a (11 a)) + b (- 13 c)$ .

$\frac{b (2 a (11 a) - 13 c)}{11 a c}$

Rewrite using the commutative property of multiplication.

$\frac{b (2 \cdot 11 a \cdot a - 13 c)}{11 a c}$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$\frac{b (2 \cdot 11 (a \cdot a) - 13 c)}{11 a c}$

Multiply $a$ by $a$ .

$\frac{b (2 \cdot 11 a^{2} - 13 c)}{11 a c}$

Multiply $2$ by $11$ .

$\frac{b (22 a^{2} - 13 c)}{11 a c}$