Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

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

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

Step 1.1.2

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

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

Step 1.1.3

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

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

Step 1.2

Cancel the common factor of $v - 3$ .

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Step 1.2.1

Cancel the common factor.

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

Step 1.2.2

Rewrite the expression.

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

Step 2

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

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

Step 3

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

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

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

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Step 5.1

Move $v$ .

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

Step 5.2

Multiply $v$ by $v$ .

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