After you clear the fractions, you will get an equation with parentheses on both sides. Expand each side and then collect all the $x$ terms on one side.

Once you have an equation of the form $(\text{number involving }k)\cdot x = (\text{other expression in }k)$, factor out $x$ if needed and then divide to solve for $x$.

Choose an easy positive value for $k$ that does not make any denominator zero (so avoid $k=0$ and $k=6$). For example, type k = 3 in Desmos to fix $k$ at 3.

In Desmos, define four separate expressions using your chosen $k$, such as xA = (2k+3)/(6-k), xB = (2k-3)/(6-k), xC = (6-k)/(2k+3), and xD = (2k+3)/(k-6). Desmos will show numerical values for each of these.

For each candidate (for example, xA), type 3/k and (xA+2)/(2*xA-1) as two separate expressions and compare their numerical values. Repeat for xB, xC, and xD. The choice whose $x$ value makes $3/k$ and $(x+2)/(2x-1)$ equal is the correct expression for $x$ in terms of $k$.

The equation is

Because this is a proportion (one fraction equals another), multiply both sides by $k(2x-1)$ to eliminate denominators:

Now expand both sides:

So the equation becomes

Get all the $x$ terms on one side and constants on the other. Subtract $kx$ from both sides and add $3$ to both sides:

Factor $x$ on the left:

To isolate $x$, divide both sides by $(6 - k)$ (note $k \neq 6$ so the denominator is not zero):

This expression matches choice A: $x = \dfrac{2k+3}{6-k}$. This is the correct way to express $x$ in terms of $k$.