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

$\frac{5 v}{2} - \frac{v - 3}{2 v^{2} - 6 v}$

Simplify each term.

Factor $2 v$ out of $2 v^{2} - 6 v$ .

Factor $2 v$ out of $2 v^{2}$ .

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

Factor $2 v$ out of $- 6 v$ .

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

Factor $2 v$ out of $2 v (v) + 2 v (- 3)$ .

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

Cancel the common factor of $v - 3$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{5 v}{2} - \frac{1}{2 v}$

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

$\frac{5 v}{2} \cdot \frac{v}{v} - \frac{1}{2 v}$

Multiply $\frac{5 v}{2}$ by $\frac{v}{v}$ .

$\frac{5 v \cdot v}{2 v} - \frac{1}{2 v}$

Combine the numerators over the common denominator.

$\frac{5 v \cdot v - 1}{2 v}$

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

Move $v$ .

$\frac{5 (v \cdot v) - 1}{2 v}$

Multiply $v$ by $v$ .

$\frac{5 v^{2} - 1}{2 v}$