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

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

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{1}{a+1}\text{, }&a\neq -1\\x\in \mathrm{C}\text{, }&a=1\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

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

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

Add 1 to both sides. Anything plus zero gives itself.

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

Subtract a from both sides.

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

Combine all terms containing x.

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

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

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

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

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

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

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

Solve for x

$$\left\{\begin{matrix}x=-\frac{1}{a+1}\text{, }&a\neq -1\\x\in \mathrm{R}\text{, }&a=1\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

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

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

Add 1 to both sides. Anything plus zero gives itself.

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

Subtract a from both sides.

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

Combine all terms containing x.

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

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

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

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

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

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

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

Solve for a

$$\left\{\begin{matrix}\\a=1\text{, }&\text{unconditionally}\\a=-1-\frac{1}{x}\text{, }&x\neq 0\end{matrix}\right.$$