Solve (a-b)x=-a+b

$$( a - b ) x = - a + b$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply a-b by x.

$$ax-bx=-a+b$$

Add a to both sides.

$$ax-bx+a=b$$

Add bx to both sides.

$$ax+a=b+bx$$

Combine all terms containing a.

$$\left(x+1\right)a=b+bx$$

The equation is in standard form.

$$\left(x+1\right)a=bx+b$$

Divide both sides by 1+x.

$$\frac{\left(x+1\right)a}{x+1}=\frac{bx+b}{x+1}$$

Dividing by 1+x undoes the multiplication by 1+x.

$$a=\frac{bx+b}{x+1}$$

Divide b+bx by 1+x.

$$a=b$$

Solve for b (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply a-b by x.

$$ax-bx=-a+b$$

Subtract b from both sides.

$$ax-bx-b=-a$$

Subtract ax from both sides.

$$-bx-b=-a-ax$$

Combine all terms containing b.

$$\left(-x-1\right)b=-a-ax$$

The equation is in standard form.

$$\left(-x-1\right)b=-ax-a$$

Divide both sides by -x-1.

$$\frac{\left(-x-1\right)b}{-x-1}=-\frac{a\left(x+1\right)}{-x-1}$$

Dividing by -x-1 undoes the multiplication by -x-1.

$$b=-\frac{a\left(x+1\right)}{-x-1}$$

Divide -a\left(1+x\right) by -x-1.

$$b=a$$

Solve for a

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

Steps for Solving Linear Equation

Use the distributive property to multiply a-b by x.

$$ax-bx=-a+b$$

Add a to both sides.

$$ax-bx+a=b$$

Add bx to both sides.

$$ax+a=b+bx$$

Combine all terms containing a.

$$\left(x+1\right)a=b+bx$$

The equation is in standard form.

$$\left(x+1\right)a=bx+b$$

Divide both sides by 1+x.

$$\frac{\left(x+1\right)a}{x+1}=\frac{bx+b}{x+1}$$

Dividing by 1+x undoes the multiplication by 1+x.

$$a=\frac{bx+b}{x+1}$$

Divide b+bx by 1+x.

$$a=b$$

Solve for b

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

Steps for Solving Linear Equation

Use the distributive property to multiply a-b by x.

$$ax-bx=-a+b$$

Subtract b from both sides.

$$ax-bx-b=-a$$

Subtract ax from both sides.

$$-bx-b=-a-ax$$

Combine all terms containing b.

$$\left(-x-1\right)b=-a-ax$$

The equation is in standard form.

$$\left(-x-1\right)b=-ax-a$$

Divide both sides by -x-1.

$$\frac{\left(-x-1\right)b}{-x-1}=-\frac{a\left(x+1\right)}{-x-1}$$

Dividing by -x-1 undoes the multiplication by -x-1.

$$b=-\frac{a\left(x+1\right)}{-x-1}$$

Divide -a\left(1+x\right) by -x-1.

$$b=a$$