Solve 1/ax=a(x-sqrt{3})

$$\frac { 1 } { a } x = a ( x - \sqrt { 3 } )$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{3}a^{2}}{1-a^{2}}$$

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

Steps for Solving Linear Equation

Multiply both sides of the equation by a.

$$1x=a\left(x-\sqrt{3}\right)a$$

Multiply a and a to get a^{2}.

$$1x=a^{2}\left(x-\sqrt{3}\right)$$

Use the distributive property to multiply a^{2} by x-\sqrt{3}.

$$1x=a^{2}x-a^{2}\sqrt{3}$$

Subtract a^{2}x from both sides.

$$1x-a^{2}x=-a^{2}\sqrt{3}$$

Reorder the terms.

$$x-xa^{2}=-\sqrt{3}a^{2}$$

Reorder the terms.

$$-xa^{2}+x=-\sqrt{3}a^{2}$$

Combine all terms containing x.

$$\left(-a^{2}+1\right)x=-\sqrt{3}a^{2}$$

The equation is in standard form.

$$\left(1-a^{2}\right)x=-\sqrt{3}a^{2}$$

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

$$\frac{\left(1-a^{2}\right)x}{1-a^{2}}=-\frac{\sqrt{3}a^{2}}{1-a^{2}}$$

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

$$x=-\frac{\sqrt{3}a^{2}}{1-a^{2}}$$

Solve for x

$$x=-\frac{\sqrt{3}a^{2}}{1-a^{2}}$$

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

Steps for Solving Linear Equation

Multiply both sides of the equation by a.

$$1x=a\left(x-\sqrt{3}\right)a$$

Multiply a and a to get a^{2}.

$$1x=a^{2}\left(x-\sqrt{3}\right)$$

Use the distributive property to multiply a^{2} by x-\sqrt{3}.

$$1x=a^{2}x-a^{2}\sqrt{3}$$

Subtract a^{2}x from both sides.

$$1x-a^{2}x=-a^{2}\sqrt{3}$$

Reorder the terms.

$$x-xa^{2}=-\sqrt{3}a^{2}$$

Reorder the terms.

$$-xa^{2}+x=-\sqrt{3}a^{2}$$

Combine all terms containing x.

$$\left(-a^{2}+1\right)x=-\sqrt{3}a^{2}$$

The equation is in standard form.

$$\left(1-a^{2}\right)x=-\sqrt{3}a^{2}$$

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

$$\frac{\left(1-a^{2}\right)x}{1-a^{2}}=-\frac{\sqrt{3}a^{2}}{1-a^{2}}$$

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

$$x=-\frac{\sqrt{3}a^{2}}{1-a^{2}}$$

Solve for a (complex solution)

$$a=-i\left(-x+\sqrt{3}\right)^{-\frac{1}{2}}\sqrt{x}$$

$$a=i\left(-x+\sqrt{3}\right)^{-\frac{1}{2}}\sqrt{x}\text{, }x\neq 0\text{ and }x\neq \sqrt{3}$$

Solve for a

$$a=\sqrt{-\frac{x}{-x+\sqrt{3}}}$$

$$a=-\sqrt{-\frac{x}{-x+\sqrt{3}}}\text{, }x<0\text{ or }x>\sqrt{3}$$