Question

Find the answer for this sum.


`(1)/(1+1/x) + (1)/(1+x)`

Obs: Please explain it to me with details.

Answer 1

The sum is 1

Explanation:

We want to find the sum of

`(1)/(1+ (1)/(x) ) + (1)/(1+x)`

Let us collect LCM for the first fraction:

`(1)/( (x + 1)/(x) ) + (1)/(1+x)`

We again reciprocate the first fraction to get:

`(x )/(x + 1) + (1)/(1+x)`

Note that the denominators are the same or rewrite to see clearly:

`(x )/( 1 + x) + (1)/(1+x)`

We can now add the exponents:

`(x + 1)/(x + 1) = 1`