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

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

• A. √(10s + q)
• B. √[-qs / (q + s)]
• C. √(2s)
• D. √[qs + (q + s)]

Answer: (D)

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

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