Solve ax-4x/a^2+a-2=1/a-1

$$\frac { a x - 4 x } { a ^ { 2 } + a - 2 } = \frac { 1 } { a - 1 }$$

Solve for a (complex solution)

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

$$x\neq 0\text{ and }x\neq 1\text{ and }x\neq -1$$

Steps for Solving Linear Equation

Variable a cannot be equal to any of the values -2,1 since division by zero is not defined. Multiply both sides of the equation by \left(a-1\right)\left(a+2\right), the least common multiple of a^{2}+a-2,a-1.

$$ax-4x=a+2$$

Subtract a from both sides.

$$ax-4x-a=2$$

Add 4x to both sides.

$$ax-a=2+4x$$

Combine all terms containing a.

$$\left(x-1\right)a=2+4x$$

The equation is in standard form.

$$\left(x-1\right)a=4x+2$$

Divide both sides by -1+x.

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

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

$$a=\frac{4x+2}{x-1}$$

Divide 2+4x by -1+x.

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

Variable a cannot be equal to any of the values -2,1.

$$a=\frac{2\left(2x+1\right)}{x-1}\text{, }a\neq -2\text{ and }a\neq 1$$

Solve for x (complex solution)

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

$$a\neq 4\text{ and }a\neq -2\text{ and }a\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(a-1\right)\left(a+2\right), the least common multiple of a^{2}+a-2,a-1.

$$ax-4x=a+2$$

Combine all terms containing x.

$$\left(a-4\right)x=a+2$$

Divide both sides by a-4.

$$\frac{\left(a-4\right)x}{a-4}=\frac{a+2}{a-4}$$

Dividing by a-4 undoes the multiplication by a-4.

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

Solve for a

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

$$x\neq 0\text{ and }|x|\neq 1$$

Steps for Solving Linear Equation

Variable a cannot be equal to any of the values -2,1 since division by zero is not defined. Multiply both sides of the equation by \left(a-1\right)\left(a+2\right), the least common multiple of a^{2}+a-2,a-1.

$$ax-4x=a+2$$

Subtract a from both sides.

$$ax-4x-a=2$$

Add 4x to both sides.

$$ax-a=2+4x$$

Combine all terms containing a.

$$\left(x-1\right)a=2+4x$$

The equation is in standard form.

$$\left(x-1\right)a=4x+2$$

Divide both sides by -1+x.

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

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

$$a=\frac{4x+2}{x-1}$$

Divide 2+4x by -1+x.

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

Variable a cannot be equal to any of the values -2,1.

$$a=\frac{2\left(2x+1\right)}{x-1}\text{, }a\neq -2\text{ and }a\neq 1$$

Solve for x

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

$$a\neq 4\text{ and }a\neq 1\text{ and }a\neq -2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(a-1\right)\left(a+2\right), the least common multiple of a^{2}+a-2,a-1.

$$ax-4x=a+2$$

Combine all terms containing x.

$$\left(a-4\right)x=a+2$$

Divide both sides by a-4.

$$\frac{\left(a-4\right)x}{a-4}=\frac{a+2}{a-4}$$

Dividing by a-4 undoes the multiplication by a-4.

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