(tan(<em>x</em>) + cot(<em>x</em>)) / (tan(<em>x</em>) - cot(<em>x</em>)) = (tan²(<em>x</em>) + 1) / (tan²(<em>x</em>) - 1)
… = (sin²(<em>x</em>) + cos²(<em>x</em>)) / (sin²(<em>x</em>) - cos²(<em>x</em>))
… = -1/cos(2<em>x</em>)
Then as <em>x</em> approaches <em>π</em>/2, the limit is -1/cos(2•<em>π</em>/2) = -sec(<em>π</em>) = 1.
It will go in it 9 times cause 9*20=180
That's definitely an example of exponential decay, since the base (1/2) (also called the "common ratio") is greater than 0 but less than 1.
Answer:
The answer to your question is (x + 3)
Step-by-step explanation:

Factor the expression

Simplify
Cancel 5 because is in both numerator and denominator
Cancel (x + 1) because is in both numerator and denominator
Cancel (x - 1) because is in both numerator and denominator
Cancel x² because is in both numerator and denominator
After simplifying, the result is (x + 3)