Answer:
The sum is 1
Step-by-step explanation:
We want to find the sum of
[tex]\frac{1}{1+ \frac{1}{x} } + \frac{1}{1+x}[/tex]
Let us collect LCM for the first fraction:
[tex]\frac{1}{ \frac{x + 1}{x} } + \frac{1}{1+x}[/tex]
We again reciprocate the first fraction to get:
[tex] \frac{x }{x + 1} + \frac{1}{1+x}[/tex]
Note that the denominators are the same or rewrite to see clearly:
[tex]\frac{x }{ 1 + x} + \frac{1}{1+x}[/tex]
We can now add the exponents:
[tex]\frac{x + 1}{x + 1} = 1[/tex]
