The value of [ 1 + 1x + 1 ] [ 1 + 1x + 2 ] [ 1 + 1x + 3 ] [ 1 + 1x + 4 ] is = ?

Answer: Option A

$$\left[1+\frac{1}{x+1}\right]$$ $$\left[1+\frac{1}{x+2}\right]$$ $$\left[1+\frac{1}{x+3}\right]$$ $$\left[1+\frac{1}{x+4}\right]$$
$$=\left[\frac{\left(x+1\right)+1}{x+1}\right]$$  $$\left[\frac{\left(x+2\right)+1}{x+2}\right]$$ $$\left[\frac{\left(x+3\right)+1}{x+3}\right]$$ $$\left[\frac{\left(x+4\right)+1}{x+4}\right]$$
$$\begin{array}{rl}& =\left(\frac{x+2}{x+1}\right)\left(\frac{x+3}{x+2}\right)\left(\frac{x+4}{x+3}\right)\left(\frac{x+5}{x+4}\right)\\ & =\frac{x+5}{x+1}\end{array}$$