Solve x-3a/a^2-2a-x/ab=-1/a

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

Solve for b

$$\left\{\begin{matrix}b=-a\text{, }&a\neq 0\\b\neq 0\text{, }&a=\frac{x}{2}\text{ and }x\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by ba^{2}, the least common multiple of a^{2},ab,a.

$$b\left(x-3a\right)-a\left(2a-x\right)=ba\left(-1\right)$$

Use the distributive property to multiply b by x-3a.

$$bx-3ba-a\left(2a-x\right)=ba\left(-1\right)$$

Use the distributive property to multiply a by 2a-x.

$$bx-3ba-\left(2a^{2}-ax\right)=ba\left(-1\right)$$

To find the opposite of 2a^{2}-ax, find the opposite of each term.

$$bx-3ba-2a^{2}+ax=ba\left(-1\right)$$

Subtract ba\left(-1\right) from both sides.

$$bx-3ba-2a^{2}+ax-ba\left(-1\right)=0$$

Combine -3ba and -ba\left(-1\right) to get -2ba.

$$bx-2ba-2a^{2}+ax=0$$

Add 2a^{2} to both sides. Anything plus zero gives itself.

$$bx-2ba+ax=2a^{2}$$

Subtract ax from both sides.

$$bx-2ba=2a^{2}-ax$$

Combine all terms containing b.

$$\left(x-2a\right)b=2a^{2}-ax$$

Divide both sides by x-2a.

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

Dividing by x-2a undoes the multiplication by x-2a.

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

Divide a\left(2a-x\right) by x-2a.

$$b=-a$$

Variable b cannot be equal to 0.

$$b=-a\text{, }b\neq 0$$

Solve for a

$$\left\{\begin{matrix}a=\frac{x}{2}\text{, }&x\neq 0\text{ and }b\neq 0\\a=-b\text{, }&b\neq 0\end{matrix}\right.$$