Question

Make s the subject of the relation : p= s + sm²/nr.

Answer 1

To make \( s \) the subject of the equation \( p = s + \frac{sm^2}{nr} \), follow these steps:

1. Start with the equation:
\[
p = s + \frac{sm^2}{nr}
\]

2. Factor \( s \) out of the right-hand side:
\[
p = s \left( 1 + \frac{m^2}{nr} \right)
\]

3. Isolate \( s \) by dividing both sides by \( \left( 1 + \frac{m^2}{nr} \right) \):
\[
s = \frac{p}{1 + \frac{m^2}{nr}}
\]

4. To simplify this further, we can combine the terms in the denominator:
\[
s = \frac{p}{\frac{nr + m^2}{nr}}
\]

5. Simplifying it gives:
\[
s = \frac{p \cdot nr}{nr + m^2}
\]

Thus, the final expression with \( s \) as the subject is:
\[
s = \frac{p \cdot nr}{nr + m^2}
\]