Answer
$1+\dfrac{1}{1+\dfrac{1}{1+x}}=\dfrac{2x+3}{x+2}$
Work Step by Step
$1+\dfrac{1}{1+\dfrac{1}{1+x}}$
Evaluate the sum in the denominator of the fraction:
$1+\dfrac{1}{1+\dfrac{1}{1+x}}=1+\dfrac{1}{\dfrac{(1+x)+1}{1+x}}=1+\dfrac{1}{\dfrac{x+2}{x+1}}=...$
Evaluate the division:
$...=1+\dfrac{x+1}{x+2}=...$
Finally, evaluate the sum and simplify:
$...=\dfrac{(x+2)+(x+1)}{x+2}=\dfrac{2x+3}{x+2}$
