Simplify 5/(2b)-(b+4)/(2b^2-2b)

$\frac{5}{2 b} - \frac{b + 4}{2 b^{2} - 2 b}$

Step 1

Factor $2 b$ out of $2 b^{2} - 2 b$ .

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

$\frac{5}{2 b} - \frac{b + 4}{2 b (b) - 2 b}$

Factor $2 b$ out of $- 2 b$ .

$\frac{5}{2 b} - \frac{b + 4}{2 b (b) + 2 b (- 1)}$

Factor $2 b$ out of $2 b (b) + 2 b (- 1)$ .

$\frac{5}{2 b} - \frac{b + 4}{2 b (b - 1)}$

Step 2

To write $\frac{5}{2 b}$ as a fraction with a common denominator, multiply by $\frac{b - 1}{b - 1}$ .

$\frac{5}{2 b} \cdot \frac{b - 1}{b - 1} - \frac{b + 4}{2 b (b - 1)}$

Step 3

Simplify terms.

Multiply $\frac{5}{2 b}$ by $\frac{b - 1}{b - 1}$ .

$\frac{5 (b - 1)}{2 b (b - 1)} - \frac{b + 4}{2 b (b - 1)}$

Combine the numerators over the common denominator.

$\frac{5 (b - 1) - (b + 4)}{2 b (b - 1)}$

Step 4

Simplify the numerator.

Apply the distributive property.

$\frac{5 b + 5 \cdot - 1 - (b + 4)}{2 b (b - 1)}$

Multiply $5$ by $- 1$ .

$\frac{5 b - 5 - (b + 4)}{2 b (b - 1)}$

Apply the distributive property.

$\frac{5 b - 5 - b - 1 \cdot 4}{2 b (b - 1)}$

Multiply $- 1$ by $4$ .

$\frac{5 b - 5 - b - 4}{2 b (b - 1)}$

Subtract $b$ from $5 b$ .

$\frac{4 b - 5 - 4}{2 b (b - 1)}$

Subtract $4$ from $- 5$ .

$\frac{4 b - 9}{2 b (b - 1)}$