How can you solve for b in the equation [b² - (q + s)] / q = s?

To solve for b in the equation ([b² - (q + s)] / q = s), we should manipulate the expression to isolate (b²). The first step involves multiplying both sides of the equation by (q) to eliminate the denominator, resulting in (b² - (q + s) = sq).

Next, we can rearrange the equation as follows:

[b² = sq + (q + s)]

This simplifies further to:

[b² = sq + q + s]

Combining like terms gives us:

[b² = q(s + 1) + s]

Now, to express (b) in terms of (q) and (s), we would take the square root of both sides.

By analyzing the correct answer, we find that it suggests a rational combination of the terms involving (q) and (s). Specifically, we can rearrange the pieces in the final equation (q(s + 1) + s) to align with one of the expressions where the square root component accounts for these terms.

The correct expression suggests a formulation that can indeed accurately represent the consolidated terms from our earlier