Solve 4E/x+90=E/x

$$\frac{ 4E }{ x+90 } = \frac{ E }{ x }$$

Solve for E (complex solution)

$$\left\{\begin{matrix}E=0\text{, }&x\neq -90\text{ and }x\neq 0\\E\in \mathrm{C}\text{, }&x=30\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x\left(x+90\right), the least common multiple of x+90,x.

$$x\times 4E=\left(x+90\right)E$$

Use the distributive property to multiply x+90 by E.

$$x\times 4E=xE+90E$$

Subtract xE from both sides.

$$x\times 4E-xE=90E$$

Combine x\times 4E and -xE to get 3xE.

$$3xE=90E$$

Subtract 90E from both sides.

$$3xE-90E=0$$

Combine all terms containing E.

$$\left(3x-90\right)E=0$$

Divide 0 by 3x-90.

$$E=0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=30\text{, }&\text{unconditionally}\\x\in \mathrm{C}\setminus -90,0\text{, }&E=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -90,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+90\right), the least common multiple of x+90,x.

$$x\times 4E=\left(x+90\right)E$$

Use the distributive property to multiply x+90 by E.

$$x\times 4E=xE+90E$$

Subtract xE from both sides.

$$x\times 4E-xE=90E$$

Combine x\times 4E and -xE to get 3xE.

$$3xE=90E$$

The equation is in standard form.

$$3Ex=90E$$

Divide both sides by 3E.

$$\frac{3Ex}{3E}=\frac{90E}{3E}$$

Dividing by 3E undoes the multiplication by 3E.

$$x=\frac{90E}{3E}$$

Divide 90E by 3E.

$$x=30$$

Solve for E

$$\left\{\begin{matrix}E=0\text{, }&x\neq -90\text{ and }x\neq 0\\E\in \mathrm{R}\text{, }&x=30\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x\left(x+90\right), the least common multiple of x+90,x.

$$x\times 4E=\left(x+90\right)E$$

Use the distributive property to multiply x+90 by E.

$$x\times 4E=xE+90E$$

Subtract xE from both sides.

$$x\times 4E-xE=90E$$

Combine x\times 4E and -xE to get 3xE.

$$3xE=90E$$

Subtract 90E from both sides.

$$3xE-90E=0$$

Combine all terms containing E.

$$\left(3x-90\right)E=0$$

Divide 0 by 3x-90.

$$E=0$$

Solve for x

$$\left\{\begin{matrix}\\x=30\text{, }&\text{unconditionally}\\x\in \mathrm{R}\setminus -90,0\text{, }&E=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -90,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+90\right), the least common multiple of x+90,x.

$$x\times 4E=\left(x+90\right)E$$

Use the distributive property to multiply x+90 by E.

$$x\times 4E=xE+90E$$

Subtract xE from both sides.

$$x\times 4E-xE=90E$$

Combine x\times 4E and -xE to get 3xE.

$$3xE=90E$$

The equation is in standard form.

$$3Ex=90E$$

Divide both sides by 3E.

$$\frac{3Ex}{3E}=\frac{90E}{3E}$$

Dividing by 3E undoes the multiplication by 3E.

$$x=\frac{90E}{3E}$$

Divide 90E by 3E.

$$x=30$$