Simplify 3/(4v^2+4v)-7/2

$\frac{3}{4 v^{2} + 4 v} - \frac{7}{2}$

Step 1

Factor $4 v$ out of $4 v^{2} + 4 v$ .

Factor $4 v$ out of $4 v^{2}$ .

$\frac{3}{4 v (v) + 4 v} - \frac{7}{2}$

Factor $4 v$ out of $4 v$ .

$\frac{3}{4 v (v) + 4 v (1)} - \frac{7}{2}$

Factor $4 v$ out of $4 v (v) + 4 v (1)$ .

$\frac{3}{4 v (v + 1)} - \frac{7}{2}$

Step 2

To write $- \frac{7}{2}$ as a fraction with a common denominator, multiply by $\frac{2 v (v + 1)}{2 v (v + 1)}$ .

$\frac{3}{4 v (v + 1)} - \frac{7}{2} \cdot \frac{2 v (v + 1)}{2 v (v + 1)}$

Step 3

Write each expression with a common denominator of $4 v (v + 1)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{7}{2}$ by $\frac{2 v (v + 1)}{2 v (v + 1)}$ .

$\frac{3}{4 v (v + 1)} - \frac{7 (2 v (v + 1))}{2 (2 v (v + 1))}$

Multiply $2$ by $2$ .

$\frac{3}{4 v (v + 1)} - \frac{7 (2 v (v + 1))}{4 (v (v + 1))}$

Reorder the factors of $4 (v (v + 1))$ .

$\frac{3}{4 v (v + 1)} - \frac{7 (2 v (v + 1))}{4 v (v + 1)}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 - 7 (2 v (v + 1))}{4 v (v + 1)}$

Step 5

Simplify the numerator.

Multiply $- 7$ by $2$ .

$\frac{3 - 14 v (v + 1)}{4 v (v + 1)}$

Apply the distributive property.

$\frac{3 - 14 v \cdot v - 14 v \cdot 1}{4 v (v + 1)}$

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

Move $v$ .

$\frac{3 - 14 (v \cdot v) - 14 v \cdot 1}{4 v (v + 1)}$

Multiply $v$ by $v$ .

$\frac{3 - 14 v^{2} - 14 v \cdot 1}{4 v (v + 1)}$

Multiply $- 14$ by $1$ .

$\frac{3 - 14 v^{2} - 14 v}{4 v (v + 1)}$

Reorder terms.

$\frac{- 14 v^{2} - 14 v + 3}{4 v (v + 1)}$

Step 6

Simplify with factoring out.

Factor $- 1$ out of $- 14 v^{2}$ .

$\frac{- (14 v^{2}) - 14 v + 3}{4 v (v + 1)}$

Factor $- 1$ out of $- 14 v$ .

$\frac{- (14 v^{2}) - (14 v) + 3}{4 v (v + 1)}$

Factor $- 1$ out of $- (14 v^{2}) - (14 v)$ .

$\frac{- (14 v^{2} + 14 v) + 3}{4 v (v + 1)}$

Rewrite $3$ as $- 1 (- 3)$ .

$\frac{- (14 v^{2} + 14 v) - 1 (- 3)}{4 v (v + 1)}$

Factor $- 1$ out of $- (14 v^{2} + 14 v) - 1 (- 3)$ .

$\frac{- (14 v^{2} + 14 v - 3)}{4 v (v + 1)}$

Simplify the expression.

Rewrite $- (14 v^{2} + 14 v - 3)$ as $- 1 (14 v^{2} + 14 v - 3)$ .

$\frac{- 1 (14 v^{2} + 14 v - 3)}{4 v (v + 1)}$

Move the negative in front of the fraction.

$- \frac{14 v^{2} + 14 v - 3}{4 v (v + 1)}$

Simplify 3/(4v^2+4v)-7/2

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