Solve =P(k^2+2)/k^2=3/2P

$$= \frac { P ( k ^ { 2 } + 2 ) } { k ^ { 2 } } = \frac { 3 } { 2 } P$$

Solve for P (complex solution)

$$\left\{\begin{matrix}P=0\text{, }&k\neq 0\\P\in \mathrm{C}\text{, }&k=-2\text{ or }k=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2k^{2}, the least common multiple of k^{2},2.

$$2P\left(k^{2}+2\right)=\frac{3}{2}P\times 2k^{2}$$

Use the distributive property to multiply 2P by k^{2}+2.

$$2Pk^{2}+4P=\frac{3}{2}P\times 2k^{2}$$

Multiply \frac{3}{2} and 2 to get 3.

$$2Pk^{2}+4P=3Pk^{2}$$

Subtract 3Pk^{2} from both sides.

$$2Pk^{2}+4P-3Pk^{2}=0$$

Combine 2Pk^{2} and -3Pk^{2} to get -Pk^{2}.

$$-Pk^{2}+4P=0$$

Combine all terms containing P.

$$\left(-k^{2}+4\right)P=0$$

The equation is in standard form.

$$\left(4-k^{2}\right)P=0$$

Divide 0 by -k^{2}+4.

$$P=0$$

Solve for P

$$\left\{\begin{matrix}P=0\text{, }&k\neq 0\\P\in \mathrm{R}\text{, }&|k|=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2k^{2}, the least common multiple of k^{2},2.

$$2P\left(k^{2}+2\right)=\frac{3}{2}P\times 2k^{2}$$

Use the distributive property to multiply 2P by k^{2}+2.

$$2Pk^{2}+4P=\frac{3}{2}P\times 2k^{2}$$

Multiply \frac{3}{2} and 2 to get 3.

$$2Pk^{2}+4P=3Pk^{2}$$

Subtract 3Pk^{2} from both sides.

$$2Pk^{2}+4P-3Pk^{2}=0$$

Combine 2Pk^{2} and -3Pk^{2} to get -Pk^{2}.

$$-Pk^{2}+4P=0$$

Combine all terms containing P.

$$\left(-k^{2}+4\right)P=0$$

The equation is in standard form.

$$\left(4-k^{2}\right)P=0$$

Divide 0 by -k^{2}+4.

$$P=0$$

Solve for k

$$\left\{\begin{matrix}\\k=2\text{; }k=-2\text{, }&\text{unconditionally}\\k\neq 0\text{, }&P=0\end{matrix}\right.$$