Make s the subject of the relation: P = S + $\frac{sm^2}{nr}$

The relation is P = S + sm²/(nr). The capital S and small s are most likely the same variable, since the question asks for s as the subject. I'll treat the relation as P = s + sm²/(nr).

Step 1: Factor out s

P = s(1 + m²/(nr))

Step 2: Combine the terms in the bracket

1 + m²/(nr) = (nr + m²)/(nr)

So P = s(nr + m²)/(nr)

Step 3: Make s the subject

Multiply both sides by nr:

nrP = s(nr + m²)

Divide both sides by (nr + m²):

s = nrP/(nr + m²)

Check against the options

• A has mrp in the numerator, which is wrong.
• B is the inverted form, which is wrong.
• C has mr + m² in the denominator, which is wrong.
• D gives s = nrp/(nr + m²), which matches our result.

The correct answer is D.

Exam tip: When the subject appears in more than one term, collect those terms on one side and factor out the subject. Then divide by the bracket. Also check that the variable on the left matches the one in the options, because a capital S and a small s can be a typo in the question.