Simplify 3/2-6/(3v(v-5))

$\frac{3}{2} - \frac{6}{3 v (v - 5)}$

Cancel the common factor of $6$ and $3$ .

Factor $3$ out of $6$ .

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

Cancel the common factors.

Factor $3$ out of $3 v (v - 5)$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{3}{2} - \frac{2}{v (v - 5)}$

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{v (v - 5)}{v (v - 5)}$ .

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

To write $- \frac{2}{v (v - 5)}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Write each expression with a common denominator of $2 v (v - 5)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{2}$ by $\frac{v (v - 5)}{v (v - 5)}$ .

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

Multiply $\frac{2}{v (v - 5)}$ by $\frac{2}{2}$ .

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

Reorder the factors of $2 (v (v - 5))$ .

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

Reorder the factors of $v (v - 5) \cdot 2$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $v$ by $v$ by adding the exponents.

Move $v$ .

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

Multiply $v$ by $v$ .

$\frac{3 v^{2} + 3 v \cdot - 5 - 2 \cdot 2}{2 v (v - 5)}$

Multiply $- 5$ by $3$ .

$\frac{3 v^{2} - 15 v - 2 \cdot 2}{2 v (v - 5)}$

Multiply $- 2$ by $2$ .

$\frac{3 v^{2} - 15 v - 4}{2 v (v - 5)}$