Algebra Question on $\theta + \frac{1}{\theta} = \frac{\theta}{1+ \theta^2}.$

Question

Answer for one of my tutorial question was $$\theta + \dfrac{1}{\theta} = \dfrac{\theta}{1+ \theta^2}.$$ But, I quite confuse because shouldn't it be like $$\theta + \dfrac{1}{\theta} = \dfrac{\theta^2 + 1}{\theta}.$$ How come it got $\dfrac{\theta}{1+ \theta^2}$?

Can anyone explain it to me?

Answer 1

You are correct

$$ θ+(1/θ)=(θ^2+1)/θ \neq θ/(1+θ^2) $$

Sometimes misprints happen is books or notes.