Simplify ((e^2-f^2)/(ef))/((e-f)/f)

$\frac{\frac{e^{2} - f^{2}}{e f}}{\frac{e - f}{f}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{e^{2} - f^{2}}{e f} \cdot \frac{f}{e - f}$

Simplify terms.

Cancel the common factor of $f$ .

Factor $f$ out of $e f$ .

$\frac{e^{2} - f^{2}}{f e} \cdot \frac{f}{e - f}$

Cancel the common factor.

$\frac{e^{2} - f^{2}}{f e} \cdot \frac{f}{e - f}$

Rewrite the expression.

$\frac{e^{2} - f^{2}}{e} \cdot \frac{1}{e - f}$

Multiply $\frac{e^{2} - f^{2}}{e}$ by $\frac{1}{e - f}$ .

$\frac{e^{2} - f^{2}}{e (e - f)}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = e$ and $b = f$ .

$\frac{(e + f) (e - f)}{e (e - f)}$

Cancel the common factor of $e - f$ .

Cancel the common factor.

$\frac{(e + f) (e - f)}{e (e - f)}$

Rewrite the expression.

$\frac{e + f}{e}$