Simplify (1+(tan(theta)+1)/(tan(theta)))/(-1+(tan(theta)-1)/(tan(theta)))

$\frac{1 + \frac{\tan (θ) + 1}{\tan (θ)}}{- 1 + \frac{\tan (θ) - 1}{\tan (θ)}}$

Multiply the numerator and denominator of the complex fraction by $\tan (θ)$ .

Multiply $\frac{1 + \frac{\tan (θ) + 1}{\tan (θ)}}{- 1 + \frac{\tan (θ) - 1}{\tan (θ)}}$ by $\frac{\tan (θ)}{\tan (θ)}$ .

$\frac{\tan (θ)}{\tan (θ)} \cdot \frac{1 + \frac{\tan (θ) + 1}{\tan (θ)}}{- 1 + \frac{\tan (θ) - 1}{\tan (θ)}}$

Combine.

$\frac{\tan (θ) (1 + \frac{\tan (θ) + 1}{\tan (θ)})}{\tan (θ) (- 1 + \frac{\tan (θ) - 1}{\tan (θ)})}$

Apply the distributive property.

$\frac{\tan (θ) \cdot 1 + \tan (θ) \frac{\tan (θ) + 1}{\tan (θ)}}{\tan (θ) \cdot - 1 + \tan (θ) \frac{\tan (θ) - 1}{\tan (θ)}}$

Simplify by cancelling.

Cancel the common factor of $\tan (θ)$ .

Cancel the common factor.

$\frac{\tan (θ) \cdot 1 + \tan (θ) \frac{\tan (θ) + 1}{\tan (θ)}}{\tan (θ) \cdot - 1 + \tan (θ) \frac{\tan (θ) - 1}{\tan (θ)}}$

Rewrite the expression.

$\frac{\tan (θ) \cdot 1 + \tan (θ) + 1}{\tan (θ) \cdot - 1 + \tan (θ) \frac{\tan (θ) - 1}{\tan (θ)}}$

Cancel the common factor of $\tan (θ)$ .

Cancel the common factor.

$\frac{\tan (θ) \cdot 1 + \tan (θ) + 1}{\tan (θ) \cdot - 1 + \tan (θ) \frac{\tan (θ) - 1}{\tan (θ)}}$

Rewrite the expression.

$\frac{\tan (θ) \cdot 1 + \tan (θ) + 1}{\tan (θ) \cdot - 1 + \tan (θ) - 1}$

Simplify the numerator.

Multiply $\tan (θ)$ by $1$ .

$\frac{\tan (θ) + \tan (θ) + 1}{\tan (θ) \cdot - 1 + \tan (θ) - 1}$

Add $\tan (θ)$ and $\tan (θ)$ .

$\frac{2 \tan (θ) + 1}{\tan (θ) \cdot - 1 + \tan (θ) - 1}$

Simplify the denominator.

Move $- 1$ to the left of $\tan (θ)$ .

$\frac{2 \tan (θ) + 1}{- 1 \cdot \tan (θ) + \tan (θ) - 1}$

Rewrite $- 1 \tan (θ)$ as $- \tan (θ)$ .

$\frac{2 \tan (θ) + 1}{- \tan (θ) + \tan (θ) - 1}$

Add $- \tan (θ)$ and $\tan (θ)$ .

$\frac{2 \tan (θ) + 1}{0 - 1}$

Subtract $1$ from $0$ .

$\frac{2 \tan (θ) + 1}{- 1}$

Simplify by multiplying through.

Move the negative one from the denominator of $\frac{2 \tan (θ) + 1}{- 1}$ .

$- 1 \cdot (2 \tan (θ) + 1)$

Apply the distributive property.

$- 1 (2 \tan (θ)) - 1 \cdot 1$

Multiply.

Multiply $2$ by $- 1$ .

$- 2 \tan (θ) - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$- 2 \tan (θ) - 1$