Simplify (15a)/b-(6b)/5

$\frac{15 a}{b} - \frac{6 b}{5}$

Step 1

To write $\frac{15 a}{b}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{15 a}{b} \cdot \frac{5}{5} - \frac{6 b}{5}$

Step 2

To write $- \frac{6 b}{5}$ as a fraction with a common denominator, multiply by $\frac{b}{b}$ .

$\frac{15 a}{b} \cdot \frac{5}{5} - \frac{6 b}{5} \cdot \frac{b}{b}$

Step 3

Write each expression with a common denominator of $b \cdot 5$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{15 a}{b}$ by $\frac{5}{5}$ .

$\frac{15 a \cdot 5}{b \cdot 5} - \frac{6 b}{5} \cdot \frac{b}{b}$

Multiply $\frac{6 b}{5}$ by $\frac{b}{b}$ .

$\frac{15 a \cdot 5}{b \cdot 5} - \frac{6 b \cdot b}{5 b}$

Reorder the factors of $b \cdot 5$ .

$\frac{15 a \cdot 5}{5 b} - \frac{6 b \cdot b}{5 b}$

Step 4

Combine the numerators over the common denominator.

$\frac{15 a \cdot 5 - 6 b \cdot b}{5 b}$

Step 5

Simplify the numerator.

Factor $3$ out of $15 a \cdot 5 - 6 b \cdot b$ .

Factor $3$ out of $15 a \cdot 5$ .

$\frac{3 (5 a \cdot 5) - 6 b \cdot b}{5 b}$

Factor $3$ out of $- 6 b \cdot b$ .

$\frac{3 (5 a \cdot 5) + 3 (- 2 b \cdot b)}{5 b}$

Factor $3$ out of $3 (5 a \cdot 5) + 3 (- 2 b \cdot b)$ .

$\frac{3 (5 a \cdot 5 - 2 b \cdot b)}{5 b}$

Multiply $5$ by $5$ .

$\frac{3 (25 a - 2 b \cdot b)}{5 b}$

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

Move $b$ .

$\frac{3 (25 a - 2 (b \cdot b))}{5 b}$

Multiply $b$ by $b$ .

$\frac{3 (25 a - 2 b^{2})}{5 b}$