Solve ax+3-3a=2/a

$$a x + 3 - 3 a = \frac { 2 } { a }$$

Solve for x

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

$$a\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a.

$$axa+a\times 3-3aa=2$$

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

$$a^{2}x+a\times 3-3aa=2$$

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

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

Subtract a\times 3 from both sides.

$$a^{2}x-3a^{2}=2-a\times 3$$

Add 3a^{2} to both sides.

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

Multiply -1 and 3 to get -3.

$$a^{2}x=2-3a+3a^{2}$$

The equation is in standard form.

$$a^{2}x=3a^{2}-3a+2$$

Divide both sides by a^{2}.

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

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

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

Divide 2-3a+3a^{2} by a^{2}.

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

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{\sqrt{8x-15}-3}{2\left(x-3\right)}\text{; }a=-\frac{\sqrt{8x-15}+3}{2\left(x-3\right)}\text{, }&x\neq 3\\a=\frac{2}{3}\approx 0.666666667\text{, }&x=3\end{matrix}\right.$$

Solve for a

$$\left\{\begin{matrix}a=\frac{\sqrt{8x-15}-3}{2\left(x-3\right)}\text{; }a=-\frac{\sqrt{8x-15}+3}{2\left(x-3\right)}\text{, }&x\neq 3\text{ and }x\geq \frac{15}{8}\\a=\frac{2}{3}\approx 0.666666667\text{, }&x=3\end{matrix}\right.$$