Solve x^2(k-2)*a=x^2(k+1)

$$x ^ { 2 ( k - 2 ) } \times a = x ^ { 2 ( k + 1 ) }$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=x^{6}\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&x=0\text{ and }k\neq 2\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by k-2.

$$x^{2k-4}a=x^{2\left(k+1\right)}$$

Use the distributive property to multiply 2 by k+1.

$$x^{2k-4}a=x^{2k+2}$$

Divide both sides by x^{-4+2k}.

$$\frac{x^{2k-4}a}{x^{2k-4}}=\frac{x^{2k+2}}{x^{2k-4}}$$

Dividing by x^{-4+2k} undoes the multiplication by x^{-4+2k}.

$$a=\frac{x^{2k+2}}{x^{2k-4}}$$

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

$$a=x^{6}$$

Solve for a

$$\left\{\begin{matrix}a=x^{6}\text{, }&\left(x<0\text{ and }Denominator(2k)\text{bmod}2=1\right)\text{ or }x>0\\a\in \mathrm{R}\text{, }&x=0\text{ and }k>2\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by k-2.

$$x^{2k-4}a=x^{2\left(k+1\right)}$$

Use the distributive property to multiply 2 by k+1.

$$x^{2k-4}a=x^{2k+2}$$

Divide both sides by x^{2k-4}.

$$\frac{x^{2k-4}a}{x^{2k-4}}=\frac{x^{2k+2}}{x^{2k-4}}$$

Dividing by x^{2k-4} undoes the multiplication by x^{2k-4}.

$$a=\frac{x^{2k+2}}{x^{2k-4}}$$

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

$$a=x^{6}$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k\neq 2\text{, }&x=0\\k\in \mathrm{C}\text{, }&a=x^{6}\end{matrix}\right.$$

Solve for k

$$k\in \mathrm{R}$$

$$a=x^{6}\text{ and }x>0$$