Simplify (b-5)/(2b)*(b^2+3b)/(b-5)

$\frac{b - 5}{2 b} \cdot \frac{b^{2} + 3 b}{b - 5}$

Factor $b$ out of $b^{2} + 3 b$ .

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

$\frac{b - 5}{2 b} \cdot \frac{b \cdot b + 3 b}{b - 5}$

Factor $b$ out of $3 b$ .

$\frac{b - 5}{2 b} \cdot \frac{b \cdot b + b \cdot 3}{b - 5}$

Factor $b$ out of $b \cdot b + b \cdot 3$ .

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

Cancel the common factor of $b - 5$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{2 b} \cdot (b (b + 3))$

Cancel the common factor of $b$ .

Factor $b$ out of $2 b$ .

$\frac{1}{b \cdot 2} \cdot (b (b + 3))$

Cancel the common factor.

$\frac{1}{b \cdot 2} \cdot (b (b + 3))$

Rewrite the expression.

$\frac{1}{2} \cdot (b + 3)$

Apply the distributive property.

$\frac{1}{2} b + \frac{1}{2} \cdot 3$

Combine $\frac{1}{2}$ and $b$ .

$\frac{b}{2} + \frac{1}{2} \cdot 3$

Combine $\frac{1}{2}$ and $3$ .

$\frac{b}{2} + \frac{3}{2}$

Combine the numerators over the common denominator.

$\frac{b + 3}{2}$