Given $y=\dfrac{x}{x-1}$ and $x\gt 1$, which of the following is a possible value of $y$ ?

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Substitute each value in for $y$, and check if there is an $x$ value that could lead to the $y$ value. For example, checking the first choice.

$$-1.9=\frac{x}{x-1}$$ $$-1.9x+1.9=x$$ $$1.9=2.9x$$ $$x= \frac{1.9}{2.9}$$

Which is not possible since $x\gt 1$.

Note that if $x\gt 1$, the fraction will always be a positive number over another positive number.

$$\frac{x}{x-1} \gt 0 \text{ if } x\gt 1$$

Next, note that the numerator will always be larger than the denominator, which means that the quotient will be greater than 1.