Solve 0=a^2x-1-(x-2)

$$0 = a ^ { 2 } x - 1 - ( x - 2 )$$

Solve for x (complex solution)

$$x=-\frac{1}{a^{2}-1}$$

$$a\neq -1\text{ and }a\neq 1$$

Steps for Solving Linear Equation

To find the opposite of x-2, find the opposite of each term.

$$0=a^{2}x-1-x+2$$

Add -1 and 2 to get 1.

$$0=a^{2}x+1-x$$

Swap sides so that all variable terms are on the left hand side.

$$a^{2}x+1-x=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$a^{2}x-x=-1$$

Combine all terms containing x.

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

Divide both sides by -1+a^{2}.

$$\frac{\left(a^{2}-1\right)x}{a^{2}-1}=-\frac{1}{a^{2}-1}$$

Dividing by -1+a^{2} undoes the multiplication by -1+a^{2}.

$$x=-\frac{1}{a^{2}-1}$$

Solve for x

$$x=-\frac{1}{a^{2}-1}$$

$$|a|\neq 1$$

Steps for Solving Linear Equation

To find the opposite of x-2, find the opposite of each term.

$$0=a^{2}x-1-x+2$$

Add -1 and 2 to get 1.

$$0=a^{2}x+1-x$$

Swap sides so that all variable terms are on the left hand side.

$$a^{2}x+1-x=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$a^{2}x-x=-1$$

Combine all terms containing x.

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

Divide both sides by a^{2}-1.

$$\frac{\left(a^{2}-1\right)x}{a^{2}-1}=-\frac{1}{a^{2}-1}$$

Dividing by a^{2}-1 undoes the multiplication by a^{2}-1.

$$x=-\frac{1}{a^{2}-1}$$

Solve for a (complex solution)

$$a=-\sqrt{\frac{x-1}{x}}$$

$$a=\sqrt{\frac{x-1}{x}}\text{, }x\neq 0$$

Solve for a

$$a=\sqrt{\frac{x-1}{x}}$$

$$a=-\sqrt{\frac{x-1}{x}}\text{, }x\geq 1\text{ or }x<0$$