Solve a/x+b/x=4a/x^2

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

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{bx}{x-4}\text{, }&x\neq 4\text{ and }x\neq 0\\a\in \mathrm{C}\text{, }&x=4\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x^{2}, the least common multiple of x,x^{2}.

$$xa+xb=4a$$

Subtract 4a from both sides.

$$xa+xb-4a=0$$

Subtract xb from both sides. Anything subtracted from zero gives its negation.

$$xa-4a=-xb$$

Reorder the terms.

$$ax-4a=-bx$$

Combine all terms containing a.

$$\left(x-4\right)a=-bx$$

Divide both sides by x-4.

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

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

$$a=-\frac{bx}{x-4}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{bx}{x-4}\text{, }&x\neq 4\text{ and }x\neq 0\\a\in \mathrm{R}\text{, }&x=4\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x^{2}, the least common multiple of x,x^{2}.

$$xa+xb=4a$$

Subtract 4a from both sides.

$$xa+xb-4a=0$$

Subtract xb from both sides. Anything subtracted from zero gives its negation.

$$xa-4a=-xb$$

Reorder the terms.

$$ax-4a=-bx$$

Combine all terms containing a.

$$\left(x-4\right)a=-bx$$

Divide both sides by x-4.

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

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

$$a=-\frac{bx}{x-4}$$

Solve for b

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

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x^{2}, the least common multiple of x,x^{2}.

$$xa+xb=4a$$

Subtract xa from both sides.

$$xb=4a-xa$$

The equation is in standard form.

$$xb=4a-ax$$

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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