Once you have $\dfrac{1}{B} = \dfrac{1}{k} - \dfrac{1}{A}$, use a common denominator of $kA$ to combine the two fractions into one.

After you find a single fraction equal to $\dfrac{1}{B}$, think about what operation gives you $B$ itself from $\dfrac{1}{B}$.

In Desmos, define two sliders: A = 5 and k = 2 (or any positive values with $A \neq k$). These will stand in for the parameters in the problem.

Type B = 1 / (1/k - 1/A) into Desmos. This uses the rearranged form $\frac{1}{B} = \frac{1}{k} - \frac{1}{A}$ to give a numerical value for $B$ based on your chosen $A$ and $k$.

For each option, enter the right-hand side as a separate expression, for example B1 = k*A/(k - A), B2 = (A - k)/(k*A), B3 = k*A/(A - k), B4 = (k - A)/(k*A). Compare the numeric values of B1, B2, B3, and B4 to the earlier B. The expression whose value matches B for your chosen $A$ and $k$ corresponds to the correct formula.

Start from the given equation:

Subtract $\frac{1}{A}$ from both sides to get an expression for $\frac{1}{B}$:

To subtract $\frac{1}{k}$ and $\frac{1}{A}$, use the common denominator $kA$:

So we have

If $\dfrac{1}{B} = \dfrac{A - k}{kA}$, then $B$ is the reciprocal of that fraction:

So the correct expression for $B$ in terms of $A$ and $k$ is