Question 203·Medium·Advanced Math

Because $1/B$ is positive, the equation says $1/k$ is larger than $1/A$. For positive numbers with numerator $1$, the larger fraction has the smaller denominator, so $k<A$.

Choose $A=6$ and $k=2$: both are positive, and $k<A$. Type the three lines shown. Replacing $B$ with $B_1$ names the unknown, and $\sim$ tells Desmos to fit it. Desmos reports $B_1=3$ under PARAMETERS. This is a sign check, not the general formula.

Subtract $1/A$ from both sides to isolate $1/B$, the reciprocal of $B$:

Use the common denominator $kA$. Multiply each fraction's top and bottom by the factor its bottom is missing:

The bottoms match now, so subtract only the tops:

Since $k<A$, $A-k$ is positive, so you can take the reciprocal of both sides: $B=\frac{kA}{A-k}$.Getting $1/B$ alone is not getting $B$ alone. This expresses $B$ in terms of $A$ and $k$. Choice C.