Solve 2x-1/x-3=e

$$\frac{ 2x-1 }{ x-3 } =e$$

Solve for x

$$x=-\frac{3e-1}{2-e}\approx 9.961055956$$

Steps for Solving Linear Equation

Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by x-3.

$$2x-1=e\left(x-3\right)$$

Use the distributive property to multiply e by x-3.

$$2x-1=ex-3e$$

Subtract ex from both sides.

$$2x-1-ex=-3e$$

Add 1 to both sides.

$$2x-ex=-3e+1$$

Combine all terms containing x.

$$\left(2-e\right)x=-3e+1$$

The equation is in standard form.

$$\left(2-e\right)x=1-3e$$

Divide both sides by 2-e.

$$\frac{\left(2-e\right)x}{2-e}=\frac{1-3e}{2-e}$$

Dividing by 2-e undoes the multiplication by 2-e.

$$x=\frac{1-3e}{2-e}$$

Variable x cannot be equal to 3.

$$x=\frac{1-3e}{2-e}\text{, }x\neq 3$$