Solve 5/e-f-5f/e^2-f^2=

$$\frac { 5 } { e - f } - \frac { 5 f } { e ^ { 2 } - f ^ { 2 } } =$$

Evaluate

$$\frac{5e}{e^{2}-f^{2}}$$

Short Solution Steps

Factor e^{2}-f^{2}.

$$\frac{5}{e-f}-\frac{5f}{\left(f+e\right)\left(-f+e\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of e-f and \left(f+e\right)\left(-f+e\right) is \left(f+e\right)\left(-f+e\right). Multiply \frac{5}{e-f} times \frac{f+e}{f+e}.

$$\frac{5\left(f+e\right)}{\left(f+e\right)\left(-f+e\right)}-\frac{5f}{\left(f+e\right)\left(-f+e\right)}$$

Since \frac{5\left(f+e\right)}{\left(f+e\right)\left(-f+e\right)} and \frac{5f}{\left(f+e\right)\left(-f+e\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\left(f+e\right)-5f}{\left(f+e\right)\left(-f+e\right)}$$

Do the multiplications in 5\left(f+e\right)-5f.

$$\frac{5f+5e-5f}{\left(f+e\right)\left(-f+e\right)}$$

Combine like terms in 5f+5e-5f.

$$\frac{5e}{\left(f+e\right)\left(-f+e\right)}$$

Expand \left(f+e\right)\left(-f+e\right).

$$\frac{5e}{-f^{2}+e^{2}}$$

Factor

$$\frac{5e}{e^{2}-f^{2}}$$