2.1 Solve for $$ x $$ without the use of a calculator: $$ P=\frac{3}{2} x\left(P Q^{2}-P q^{2}\right) $$

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1. We start with the equation  
   $$
   P = \frac{3}{2} x \left(PQ^2 - Pq^2\right)
   $$

2. Notice that in the parentheses, both terms have a factor of $$ P $$. Factor it out:  
   $$
   PQ^2 - Pq^2 = P \left(Q^2 - q^2\right)
   $$
   Now the equation becomes  
   $$
   P = \frac{3}{2} x \, P \left(Q^2 - q^2\right)
   $$

3. Assuming $$ P \neq 0 $$, divide both sides of the equation by $$ P $$:  
   $$
   \frac{P}{P} = \frac{3}{2} x \left(Q^2 - q^2\right) \quad \Longrightarrow \quad 1 = \frac{3}{2} x \left(Q^2 - q^2\right)
   $$

4. Solve for $$ x $$ by multiplying both sides by the reciprocal of $$\frac{3}{2}\left(Q^2 - q^2\right)$$:  
   $$
   x = \frac{2}{3\left(Q^2 - q^2\right)}
   $$

Thus, the solution for $$ x $$ is  
$$
x = \frac{2}{3\left( Q^2 - q^2 \right)}
$$
$$ x = \frac{2}{3(Q^2 - q^2)} $$

2.1 Solve for \( x \) without the use of a calculator: \[ P=\frac{3}{2} x\left(P Q^{2}-P q^{2}\right) \]

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