Question

Solving Equations Find all real solutions of the equation.

$\frac{x+1}{x-1}=\frac{3x}{3x-6}$

Short answer

The given equation has no real solution.

Step-by-step solution

Step 1. Definition of equation.

Equation is a mathematical statement in which two expressions are equal to each other.

Step 2. Given Information.

The given equation is:

$\frac{x+1}{x-1}=\frac{3x}{3x-6}$

Step 3. Solve the given equation.

Using cross multiplication, the given equation can be written as:

$\begin{array}{c}\left(x+1\right)\left(3x-6\right)=3x\left(x-1\right)\\ \left(x\right)\left(3x\right)+\left(x\right)\left(-6\right)+\left(1\right)\left(3x\right)+\left(1\right)\left(-6\right)=3x\left(x\right)+3x\left(-1\right)\\ 3x^2-6x+3x-6=3x^2-3x\\ 3x^2-3x-6-3x^2+3x=0\\ -6=0\end{array}$

The statement$-6=0$ is false because$-6\ne 0$ for all value of $x$.

Thus, the given equation has no real solution.