To simplify the expression, we can cancel out common factors in the numerator and denominator.
We notice that each term in the numerator has a factor of $(1 + 17)$, and each term in the denominator has a factor of $(1 + 19)$.
Canceling out these common factors, we are left with:
\[\frac{\left( 1 + \dfrac{17}{2} \right) \left( 1 + \dfrac{17}{3} \right) \dotsm \left( 1 + \dfrac{17}{19} \right)}{\left( X + \dfrac{19}{2} \right) \left( 1 + \dfrac{19}{3} \right) \dotsm \left( 1 + \dfrac{19}{17} \right)}.\]
Now, we can simplify the expression further by canceling out common factors in each term.
We notice that each term in the numerator has a factor of $\left( 1 + \dfrac{17}{k} \right)$, where $k$ ranges from 2 to 19.
Similarly, each term in the denominator has a factor of $\left( 1 + \dfrac{19}{k} \right)$, where $k$ ranges from 2 to 17.
Canceling out these common factors, we are left with:
\[\frac{1}{\left( X + \dfrac{19}{2} \right) \left( \dfrac{19}{3} \right) \dotsm \left( \dfrac{19}{17} \right)}.\]
To simplify this expression further, we can multiply the denominators together:
\[\frac{1}{\left( X + \dfrac{19}{2} \right) \left( \dfrac{19}{3} \right) \dotsm \left( \dfrac{19}{17} \right)} = \frac{1}{\dfrac{19}{2} \cdot \dfrac{19}{3} \cdot \dotsm \cdot \dfrac{19}{17}}.\]
Now, we can simplify the expression by dividing 19 by each denominator:
\[\frac{1}{\dfrac{19}{2} \cdot \dfrac{19}{3} \cdot \dotsm \cdot \dfrac{19}{17}} = \frac{1}{\dfrac{19!}{2 \cdot 3 \cdot \dotsm \cdot 17}}.\]
To simplify this expression further, we can multiply the numerator and denominator by the factorial of 18:
\[\frac{1}{\dfrac{19!}{2 \cdot 3 \cdot \dotsm \cdot 17}} = \frac{1 \cdot 18!}{19!}.\]
Now, we can simplify the expression by canceling out common factors in the numerator and denominator:
\[\frac{1 \cdot 18!}{19!} = \frac{1}{19}.\]
Given that the value of the expression is 1, we can write:
\[\frac{1}{19} = 1.\]
Therefore, the value of $X$ is 1.
The answer is: 1
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Compute
\[\frac{(1 + 17) \left( 1 + \dfrac{17}{2} \right) \left( 1 + \dfrac{17}{3} \right) \dotsm \left( 1 + \dfrac{17}{19} \right)}{(1 + 19) \left( X + \dfrac{19}{2} \right) \left( 1 + \dfrac{19}{3} \right) \dotsm \left( 1 + \dfrac{19}{17} \right)}.\]
If we know the answer to the above question is 1, what is the value of unknown variable X?

### Answer:
