Write the Fraction in Simplest Form (tan(pi)-tan(x))/(1+tan(pi)tan(x))

Factor ${\displaystyle -1}$ out of ${\displaystyle \tan \left(\pi \right)-\tan \left(x\right)}$.

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because tangent is negative in the second quadrant.

The exact value of ${\displaystyle \tan \left(0\right)}$ is ${\displaystyle 0}$.

Multiply ${\displaystyle -1}$ by ${\displaystyle 0}$.

Multiply ${\displaystyle -1}$ by ${\displaystyle 0}$.

Add ${\displaystyle 0}$ and ${\displaystyle \tan \left(x\right)}$.

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because tangent is negative in the second quadrant.

The exact value of ${\displaystyle \tan \left(0\right)}$ is ${\displaystyle 0}$.

Multiply ${\displaystyle -1}$ by ${\displaystyle 0}$.

Multiply ${\displaystyle 0}$ by ${\displaystyle \tan \left(x\right)}$.

Add ${\displaystyle 1}$ and ${\displaystyle 0}$.