Simplify ((b^2+7b)/8)/((b+7)/b)

$\frac{\frac{b^{2} + 7 b}{8}}{\frac{b + 7}{b}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{b^{2} + 7 b}{8} \cdot \frac{b}{b + 7}$

Factor $b$ out of $b^{2} + 7 b$ .

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

$\frac{b \cdot b + 7 b}{8} \cdot \frac{b}{b + 7}$

Factor $b$ out of $7 b$ .

$\frac{b \cdot b + b \cdot 7}{8} \cdot \frac{b}{b + 7}$

Factor $b$ out of $b \cdot b + b \cdot 7$ .

$\frac{b (b + 7)}{8} \cdot \frac{b}{b + 7}$

Cancel the common factor of $b + 7$ .

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Factor $b + 7$ out of $b (b + 7)$ .

$\frac{(b + 7) b}{8} \cdot \frac{b}{b + 7}$

Cancel the common factor.

$\frac{(b + 7) b}{8} \cdot \frac{b}{b + 7}$

Rewrite the expression.

$\frac{b}{8} b$

Combine $\frac{b}{8}$ and $b$ .

$\frac{b \cdot b}{8}$

Raise $b$ to the power of $1$ .

$\frac{b^{1} b}{8}$

Raise $b$ to the power of $1$ .

$\frac{b^{1} b^{1}}{8}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{b^{1 + 1}}{8}$

Add $1$ and $1$ .

$\frac{b^{2}}{8}$

Simplify ((b^2+7b)/8)/((b+7)/b)