Simplify (6a)/b-(7b)/2

$\frac{6 a}{b} - \frac{7 b}{2}$

Step 1

To write $\frac{6 a}{b}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{6 a}{b} \cdot \frac{2}{2} - \frac{7 b}{2}$

Step 2

To write $- \frac{7 b}{2}$ as a fraction with a common denominator, multiply by $\frac{b}{b}$ .

$\frac{6 a}{b} \cdot \frac{2}{2} - \frac{7 b}{2} \cdot \frac{b}{b}$

Step 3

Write each expression with a common denominator of $b \cdot 2$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{6 a}{b}$ by $\frac{2}{2}$ .

$\frac{6 a \cdot 2}{b \cdot 2} - \frac{7 b}{2} \cdot \frac{b}{b}$

Multiply $\frac{7 b}{2}$ by $\frac{b}{b}$ .

$\frac{6 a \cdot 2}{b \cdot 2} - \frac{7 b \cdot b}{2 b}$

Reorder the factors of $b \cdot 2$ .

$\frac{6 a \cdot 2}{2 b} - \frac{7 b \cdot b}{2 b}$

Step 4

Combine the numerators over the common denominator.

$\frac{6 a \cdot 2 - 7 b \cdot b}{2 b}$

Step 5

Simplify the numerator.

Multiply $2$ by $6$ .

$\frac{12 a - 7 b \cdot b}{2 b}$

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

$\frac{12 a - 7 (b \cdot b)}{2 b}$

Multiply $b$ by $b$ .

$\frac{12 a - 7 b^{2}}{2 b}$