Basic equation solving $t/(1+t)=1-1/(1+t)$

Question

In found this equality in my math book, could anyone explain to me why it is equal?

$t/(1+t)=1-1/(1+t)$

Answer 1

\begin{align} \frac{t}{1+t} &= 1 - \frac{1}{1+t}\\\\ &= \frac{1+t}{1+t} - \frac{1}{1+t}\\\\ &= \frac{1+t-1}{1+t}\\\\ &= \frac{t}{1+t} \end{align}

Moral of the story is; make a nice choice for the number $1$ and things often look like they should.

Answer 2

To prove this, let us add 1/(1+t) to both sides.

We get:

(t+1)/(1+t) = 1

Now obviously, t+1 = 1+t, so the left side of the equations is equal to one.