Solve x/a-1=ax+4

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

Solve for x

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

$$a\neq \frac{\sqrt{5}+1}{2}\text{ and }a\neq \frac{1-\sqrt{5}}{2}\text{ and }a\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a-1.

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

Use the distributive property to multiply ax by a-1.

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

Use the distributive property to multiply a-1 by 4.

$$x=xa^{2}-ax+4a-4$$

Subtract xa^{2} from both sides.

$$x-xa^{2}=-ax+4a-4$$

Add ax to both sides.

$$x-xa^{2}+ax=4a-4$$

Reorder the terms.

$$ax-xa^{2}+x=4a-4$$

Combine all terms containing x.

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

The equation is in standard form.

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

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

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

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

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

Divide -4+4a by 1-a^{2}+a.

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

Solve for a

$$a=-\frac{\sqrt{5x^{2}+8x+16}-x+4}{2x}$$

$$a=-\frac{-\sqrt{5x^{2}+8x+16}-x+4}{2x}\text{, }x\neq 0$$