## Precalculus: Mathematics for Calculus, 7th Edition

$1+\dfrac{1}{1+\dfrac{1}{1+x}}=\dfrac{2x+3}{x+2}$
$1+\dfrac{1}{1+\dfrac{1}{1+x}}$ 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: $...=\dfrac{(x+2)+(x+1)}{x+2}=\dfrac{2x+3}{x+2}$